Last summer, the Italian giants were interested in giving Mahrez a fresh challenge, but the two teams never came to an agreement over a fee.
However, according to The Mirror, the Serie A outfit are considering whether to make a fresh approach for the Algerian international, who still wants to leave the King Power Stadium.
In January, the 27-year-old wanted to push through a transfer to Manchester City and while it remains unclear whether City will return for the playmaker at the end of the season, they are likely to face competition.
The Foxes rejected an offer from City which is said to be in excess of £60m, and that may lead to Roma having to put together a player-plus-cash deal to try to tempt the East Midlands outfit into a sale.
Mahrez has contributed 10 goals and eight assists in 28 Premier League outings this season.