The Norwegian's job seems under threat after United were smashed 5-0 on the weekend by Liverpool at Old Trafford.
Antonio Conte was touted as a potential replacement.
The Italian is one of the best managers in the world and is currently without a job, having left Inter Milan last summer.
Manchester Evening News reported that Conte was 'open' to the possibility of replacing Solskjaer as United manager.
And it appears that the possibility of the Italian replacing Solskjaer as United manager has escalated even further in the last few hours.
According to journalist Gianluca Di Marzio, United have now made contact with Conte about the possibility of becoming their new manager.
Conte has reportedly already said yes to the challenge. He is is convinced he can do well with the team available right away.
Sir Alex Ferguson may well welcome the appointment of Conte.
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While he would no doubt be disappointed to see one of his former players lose his job, the United manager spoke highly of Conte back in 2017.
Speaking while Conte was at Chelsea, Ferguson said of him, per Sky Sports: "Fantastic, you see his energy on the pitch. There's a true saying that the team mirrors the manager, and that's what they've done with him.
"His team have stayed top of the league for so long. They lost to Arsenal and Liverpool early on, but since then they've been up."
United haven't made the final decision to sack Solskjaer just yet.
But if they come to the conclusion that they need a change, It seems as if Conte will be the next man up.