The Algeria international informed the Foxes in May that he wants to leave the club, believing that he was promised a transfer if a sufficient offer was tabled.
Arsenal had been battling for the 26-year-old's signature, but reports earlier this month suggested that they have now pulled out of a deal after being put off by his hefty asking price.
That left the door open for Roma to pounce, with the Italian side understood to have tabled an initial £20m offer which could rise with various add-ons.
Mahrez has verbally agreed to join Roma, but Goal.com reports that he is still waiting to see if Arsenal reignite their interest in the coming days.
It is claimed that the Gunners may re-enter the race for the 2015-16 PFA Player of the Year, though that will likely depend on whether they are successful with their attempt to sign Thomas Lemar from AS Monaco.