The Giallorossi who have been pursuing the Algerian International for several weeks are looking to sign a winger this summer.
The Foxes knocked back bids of €30m and €35m and sporting director, Monchi hinted yesterday that the Lupi would consider raising their offer.
“I’m satisfied with the effort the club has made to sign the player,” the Spaniard said yesterday.
“I don’t think any other club has bid over €30m, as Roma did.
“The player expressed what he wants publicly, but it’s right that we respect his club.
“In the end everything comes down to whether or not Leicester want to sell the player.”
Sky reveals Roma are determined to sign Mahrez, who wants to speak to them, and will raise their offer to €40m.