The 26-year-old scored 10 times in all competitions for the Foxes last season, with four of those coming in the Champions League en route to the quarter-finals of the tournament.
However, Mahrez revealed in May that he wanted to leave the King Power Stadium, just over 12 months after helping the East Midlanders to a shock Premier League title.
According to the Daily Mail, Roma see the Algerian as a replacement for Mohamed Salah but Leicester want around £50m for their star asset.
The report goes on to suggest that Arsenal and Liverpool have also checked on Mahrez but were deterred by Leicester's valuation of him.
Mahrez has three years left to run on the £100,000-a-week deal that he penned last year.