Pogba is currently injured and has not played for the Red Devils since December 2018.
The Frenchman has endured a topsy-turvy time at Old Trafford, following his return from Juventus in 2016.
The 26-year-old has been seriously linked with Real Madrid and a return to Juve.
Solskjaer has consistently insisted that Pogba remains a key part of his squad, despite recent injury problems adding to the speculation over his future.
However, Pogba has a big decision to make this summer, when he will have only one season remaining on his current deal.
It is claimed that Pogba might decide to sign a contract extension if Solskjaer is sacked.
Both men have reportedly fallen out, since Pogba failed to secure a move to Madrid last summer.