Liverpool have been knocked out of the FA cup after losing 2-1 to Wolves in the third round.
Raul Jimenez opened the scoring for the Wolves in 38th minute before Divock Origi restored parity, six minutes after the break. However, Wolves had the final say thanks to Reuben Neves strike in 55th minute.
Solskjaer was in the starting line-up for United’s semi-final victories over the Gunners in 1999 and 2004.
He went on to lift the trophy with the Old Trafford club on both occasions.
Monday night’s draw confirmed Arsenal as the home team.
It again recreates the classic match-up in the final 40 years ago which Arsenal won 3-2 thanks to Alan Sunderland’s late goal.
Other notable ties include two all-Premier League clashes — Crystal Palace against Tottenham and Manchester City versus Burnley.
Maurizio Sarri’s Chelsea, who won the FA Cup under Antonio Conte last season, host either Championship Sheffield Wednesday or League One Luton Town.
Non-League Barnet, the lowest- ranked club left in the competition, were handed a home tie with Brentford.
Manuel Pellegrini’s West Ham will face AFC Wimbledon, the League One side they beat 3-1 in the Carabao Cup third round in August.
That saw Pellegrini secure his first win as Hammers boss.
The winner of the replay between Newcastle and Blackburn takes on Watford at home.
Everton face a trip to London to play Millwall.