The 29-year-old is officially leaving the club when his contract expires at the end of the month.
A move to Italy would follow the footsteps of former Premier League outcasts who have excelled moving to Serie A.
Tammy Abraham, previously of Chelsea, linked up with the former Man United boss at Roma whereas Fikayo Tomori has just won the Serie A with AC Milan.
According to the Italian outlet La Gazzetta dello Sport, Roma are thinking about landing Lingard on a free transfer.
Despite a disappointing season, only scoring twice in 22 appearances, the history of the midfielder will be what clubs are looking at.
The 29-year-old has won four trophies throughout his career, including the Europa League in 2017.
Moving to the Italian league could motivate him after wonderful performances from previous products of the Premier League.
Lingard is not short of options and will be looking to revitalise his career after a difficult couple of years on the bench with the exception of a six-month loan deal at the end of last season with West Ham.
Throughout his career for the Red Devils, he appeared in 149 league matches, scoring 20 goals and earning 32 caps for England.
He has been at the club since 2000 and will be a huge miss for some of the players who have grown up with Lingard after being at the club for over 22 years.