However, reports suggest the former Chelsea boss wants a 'winning project', which is why he would NOT join Arsenal and rejected Tottenham Hotspur.
Solskjaer is under increasing pressure after United surrendered a one-goal lead away to Young Boys on Tuesday night to lose their opening Champions League group game.
Jason Cundy was on the Sports Bar immediately after the game and urged the Red Devils hierarchy to pursue a move for Conte to replace the 'utterly clueless' Norwegian.
"It exposed Ole, it did badly," he said. "I'd sack him. We know what's coming, don't we? You've got Antonio Conte out there…
"Who's the better manager? There will be a stage in the season where they'll be like 'I wish we did it earlier.'"
The 52-year-old Italian has a wealth of experience from his spell at Stamford Bridge where he won the Premier League in his first season and the FA Cup shortly before departing.
Conte is currently unemployed after leaving Inter Milan in the summer and Italian journalist Gianluca Di Marzio believes United would present an intriguing challenge for him - unlike Spurs or Arsenal.
"He would only accept a winning project," Di Marzio said. "So I don't think he would accept Arsenal and that is why he said no to Tottenham.
"I think he would only accept if say Manchester United called."
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