Thomas Tuchel, the coach at Paris Saint-Germain, has been suggested by one intermediary used by the club as next year's replacement but PSG will not allow their coach to go unless they want to replace him.
Zinedine Zidane seems less likely, given the nature of the job, which essentially requires rebuilding the squad while under a one-year transfer ban, imposed by FIFA on Friday for breaking rules in recruiting youth players from overseas.
Even if Chelsea's appeal delays the ban, the club will not have much to spend in the summer given that they are likely to be in the Europa League at best next season and have already committed £58million on buying Christian Pulisic, who is on loan at Borussia Dortmund.
Some are questioning the system they have been asked to play. Sarri has even been asked directly by one senior player whether N'Golo Kante can return to his usual holding role to add more defensive stability.
There is widespread bewilderment at the persistence with this 4-3-3 now that it has been exposed by so many teams. Training sessions seem very truncated, according to those present.
Antonio Rudiger's recent comments resonated: training is like being back at school, but not in a good way. The defensive unit may have five minutes being addressed by Sarri on positioning, while the attacking unit waits around. The roles can be reversed a few minutes later.
Sarri works principally on what is known as 'phase of play'. Essentially, it's what position to take up and which passes to look for as an opponent's attack breaks down and you transition into attack; or, as your own attack breaks down and you transition into defence. While all top coaches work obsessively on these transitions, under Sarri it has become a joyless exercise.
The decline is possibly explained by the fact that the worse Chelsea get, the more time Sarri feels he has to spend explaining instructions; conversely this has had the effect of some players engaging even less.
Some players want Sarri to adapt and play 4-2-3-1, with Kante holding alongside Jorginho and with Eden Hazard as a No 10. It would have the bonus of affording more opportunities to Callum Hudson-Odoi out wide.
However, Sarri has made it clear that in his first season he wants to stick with a core of players who he feels can understand and implement his tactics.
The problem is that even his core players now don't appear to be able to implement what he wants. Goals conceded since the new year have been a mixture of counter-attacks, set pieces and sustained pressure.
For all the focus on Jorginho, overwhelmed as a single holding midfielder, none of the back four now seem sure of their positioning and there are tactical weaknesses all around. It has been a spectacular fall from grace for Sarri. It is only 11 weeks ago that he beat City, 2-0 at home.
He seemed ready to adapt then, after two early-warning defeats to Tottenham and Wolves. Against City he had played largely on the counter-attack, though Chelsea did press City high up the pitch, so it was still recognisably Sarriball. Yet there seemed more flexibility.
Sarri himself noted admiringly that Kante played closer to Jorginho (though he still offered a surging run to score the opener). Defensively they looked a coherent unit. Just two months later, in the return fixture, they were a mess and 4-0 down in 25 minutes.
Initially, the team reacted well to Sarri. They enjoyed the change from Antonio Conte, who was similarly demanding and technical. A fresh voice seemed better. A lot of instruction and standing around was to be expected early on and players wanted to make a good impression. A run of 18 games unbeaten, with 14 wins, also gave Sarri credibility.
Sarri-ball crashed at Wembley in November, when Tottenham constantly pressed Jorginho, cutting off his supply lines while Son Heung-min exposed him for pace in defensive situations.
The win over City suggested there might be a reboot, but it didn't turn out that way. Mauricio Pochettino's blueprint was being used by more and more teams. A high press on Jorginho is now such a feature by rival teams that there is much sympathy for the play-maker.
With the attacking midfielders encouraged to make forward runs as soon as the ball is recovered, Jorginho is often isolated. Even Pep Guardiola has found it hard at times to play with a single holding midfielder. Chelsea, though, face bigger questions.
Even if the FIFA transfer ban will probably be suspended until next year due to an appeal, every club this summer will know they can add millions to the fee when managing director Marina Granovskaia comes calling to buy.
That is money Chelsea do not have. They have an owner whose visa has been revoked and who has given up on plans to rebuild Stamford Bridge just when the squad also needs rebuilding.
Hazard is set on Real Madrid (though they may be cooling on him, according to reports) and Hudson-Odoi wants to be at Bayern Munich. Willian and Pedro are out of contract in 2020 like Hazard and Hudson-Odoi, with David Luiz and Gary Cahill out of contract in the summer. Olivier Giroud will sign a one-year extension and Pulisic is arriving for £58m, but that won't leave much for further additions.
If Sarri is sacked after the final or the midweek game against Tottenham, they have to decide if assistant Gianfranco Zola should take over for the rest of the season or whether the club can persuade the FA to allow former first-team coach Steve Holland to be released from England duties.
Next season they will have to begin again, and this is when the spotlight falls on Granovskaia. She was instrumental in picking Sarri, overseeing a process which meant he was only confirmed on July 14 — hardly ideal timing. Since Michael Emenalo left the club in 2017, she has headed up recruitment.
Emenalo had tired of being the punching bag for manager and the board, caught in the middle with the impossible job of keeping the peace between the board and the likes of Jose Mourinho and Conte.
Chelsea's transfer record has been poor over the last five windows, but cast your mind back to August 2011, when Emenalo had just been appointed technical director. Roman Abramovich made it clear that the days of big subsidies were over and the club needed to be smarter in the transfer market.
It is hard to over-state what a fine job Emenalo did at that time. Had Chelsea held their nerve on his signings, they would be well placed to challenge City now. In 2011 he signed Kevin de Bruyne (21) for £8m, Thibaut Courtois (19) for £8m and Romelu Lukaku (18) for £10m.
In 2012, Eden Hazard (21) was an obvious target at £31.5m but Cesar Azpilicueta (22) at £7.9m was the type of unspectacular signing at which he excelled. The best under Emenalo came in January 2014: Mohamed Salah (21) for £14.8m.
Chelsea could have had a team with Courtois, Azpilicueta, De Bruyne, Hazard, Salah and Lukaku assembled for £80.2m in total. Add in some academy products such as Andreas Christensen, Ruben Loftus-Cheek, Hudson-Odoi and Ethan Amapadu and a manager who believed in blooding young players and they would be well set.
As it is, Emenalo's smartest signings are now at Liverpool and City because the club failed to include buy-back clauses when they let Salah and De Bruyne go. Next season their best academy graduate will likely be at Bayern Munich or PSG because they have not convinced him they are serious about his development. Somewhere they have lost sight of an admirable vision.
The innate glamour of the club and their recent history probably means they will nevertheless persuade a first-class coach to take over from Sarri - but given that the club are hardly renowned for their patience, the prospect of embarking on the long-term rebuilding that is required will hardly be approached with confidence by the next incumbent.