With Jose Mourinho's tenure looking increasingly shaky, Corriere dello Sport say both Conte and his former Juventus colleague Giuseppe Marotta could be on their way to Old Trafford.
Marotta is currently Juve's general manager but recently announced he will leave the job this month.
The Italian newspaper links Marotta with the role of sporting director - a post United have yet to create - saying he could take over football operations from chief executive Ed Woodward, who has been heavily criticised by fans in recent times.
With current manager Mourinho under pressure following a poor start to the season, which has also seen him fall out with star player Paul Pogba, Corriere dello Sport say Marotta and Conte could link up again.
The pair claimed three successive Serie A titles working in tandem at Juve, while Pogba was also at the club during their reign.
Conte, a former manager of the Italian national team, already has plenty of experience of the Premier League, something United would welcome, after he guided Chelsea to the title in his first season at Stamford Bridge.
His second campaign was less successful, with the Blues missing out on qualification for the Champions League, and he duly left in the summer, being replaced by Maurizio Sarri.