Solskjaer is not believed to be under any real pressure at this moment in time despite a disappointing run of form, with the Red Devils picking up just one point from their last three Premier League games.
However, the Norwegian's long-term future is unclear, and Conte continues to be linked with the position at Old Trafford, with the Italian keen to return to coaching after leaving Inter Milan over the summer.
According to journalist Duncan Castles, the 52-year-old is interested in replacing Solskjaer in Manchester, as he believes that he could win the Champions League at the club.
"I think there are two obvious candidates in terms of coaches who have achieved at the top level of the game, who are out of work and would be available to Manchester United without compensation fees," Castles said on the Transfer Window Podcast.
"One is Zinedine Zidane and one is Antonio Conte. Conte's position, I'm told, is that he is interested in the Manchester United job but not without restrictions.
"Antonio Conte, when he chooses his next club, wants a club where he can win the Champions League. He wants to demonstrate, he's wanted to do it for a long time, that he is one of the very best coaches in world football.
"To do that he knows he has to win the Champions League, so Manchester United are interesting because of the squad they've got, because of their status and because of the resource that is behind them."
Conte won the Serie A title with Inter last season but left the club over the summer due to disagreements with the board over their financial plans. body check tags ::