Soon after the end of last season, Mahrez revealed that he wanted to leave the King Power Stadium for a new challenge and Roma are known to be keen on signing the Algerian international as a replacement for Mohamed Salah.
However, the Italian giants have failed with two offers, and Mahrez has revealed that he is yet to hold any discussions over a switch to last season's Serie A runners-up.
The 26-year-old told Sky Sports News: "I know Roma came in, but nothing was accepted so there is little I can do.
"They are a great club who I would like to talk to but I can't until Leicester accept a deal. Leicester know my thoughts, but I will continue to give my best for the club as I always have.
"Clearly, it is flattering whenever you get linked with any big clubs, but as it stands, I have not talked to anyone as nobody has had a bid accepted but we nearly have a month left of the transfer window so we will see what happens."
Mahrez has netted 35 goals in 138 appearances in all competitions in his three-and-a-half years in the East Midlands.