The Manchester United striker will now 'assess' United's intent on pushing forward this summer before committing to discussions about his future.
The club is keen for the England international to extend his current deal for another two seasons and explored the possibility of opening up talks with him recently. However, according to The Sun, Rashford has informed the club he does not want to enter negotiations due to his concerns over the club's ambitions.
It has also been claimed that Rashford's belief in Solskjaer's capabilities has dwindled over the past couple of months following United's failure to make the top four.
The 21-year-old wants to be playing in the Champions League in the near future and Solskjaer understands investment is required in the summer if United are improving on their sixth-placed finish last season. Solskjaer is expected to oversee a mass overhaul next month as he looks to rid his squad of the dead wood and rebuild it with exciting young players.
Rashford is seen as a vital cog in Solskjaer's plans but United are currently at risk of slipping into the same problematic situation they find themselves in with David de Gea, whose contract talks remain at an impasse.
The Spaniard only has one year left on his deal and Paris Saint-Germain is expected to pile the pressure on United to sell by submitting on offer this summer.
Rashford’s contract expires at the end of next season but the club has an option to extend that by a year, which they will trigger if they cannot agree on a new deal.