According to Italian newspaper Tuttosport, the 43-year-old has been identified as a potential candidate to take over at the Premier League giants, after a sensational 18 months in charge at Juve.
Conte masterminded the club's stunning Serie A title success last season - in which they remained unbeaten - and has led his side to the top of the Italian top-flight at the midway stage of the 2012/13 campaign.
There has been plenty of speculation about the long-term future of Red Devils boss Sir Alex Ferguson, with some suggestions that the Scot could leave Old Trafford in the summer.
Pep Guardiola has been mooted as a potential successor, but the ex-Barcelona boss is keen to return to management ahead of 2013/14, while Ferguson is reportedly eager to carry on for another two years.
And, in Conte, Manchester United would have one of the most promising young managers in world football ready and waiting, when the 71-year-old's tenure - which now extends to 26 years - comes to a natural climax.