Michael Carrick, who has been Solskjaer's assistant, will take over managerial duties on a temporary basis.
The 40-year-old knows the club inside out having spent 12 years as a player at Old Trafford.
During his playing career with the Red Devils, Carrick won three Premier League titles, one FA Cup, two League Cups and one Champions League.
The former England international has received his fair share of criticism during Solskjaer's downfall but he remains one of the key contenders to take the managerial post on a permanent basis.
Darren Fletcher is another name which has been linked with the position and his price has been slashed to around 10/1.
The 37-year-old is the technical director at Manchester United having been promoted last January from his role as a first team coach.
Fletcher also enjoyed a memorable playing career at Old Trafford which lasted for 12 years and 223 appearances.
During that time, the former Scotland international helped the team to the same honours as the aforementioned Carrick.
Fletcher has received far less criticism than Carrick for the club's current troubles yet he finds himself behind the likes of Erik ten Hag and Ralf Rangnick in the betting.