The Italian club are in hot pursuit of the Algerian this summer as they try to replace Mohamed Salah, who has joined Liverpool.
Roma have earmarked Mahrez as the man to fill the boots of the Egyptian, but they have been struggling to meet Leicester's £35m asking price.
Roma's new sporting director, Monchi, has been charged with brokering a deal but so far he has proved unsuccessful.
That, according to Sky Italia, has left him frustrated and he is urging the club to provide him with more funds so he can snap Mahrez up.