The winger is ready to leave the Foxes this summer and has told the club he is hungry for a new challenge elsewhere.
Arsenal and Monaco have been linked with the Algerian, but it is Roma who are at the front of the queue.
And, according to Gazzetta dello Sport, the Italian club have moved a step closer to signing Mahrez after he agreed to join them.
Roma are said to have a provisional agreement in place with the 26-year-old regarding personal terms, but they now need to agree a transfer fee with Leicester.