According to Goal, the Algerian magician wants to move to the Gunners but could find his way to Italy if manager Arsene Wenger passes on his signature.
"Mahrez is impressed by the Giallorossi's determination to bring him to Stadio Olimpico but would prefer to turn out for the Gunners should the opportunity arise.
"It is understood that Roma sporting director Monchi has prepared a very lucrative financial package for the Leicester star, which has turned the player's head towards a league no longer considered to be among the best in the world."
However, things may not be so cut and dried; according to Sky Sports' Kaveh Solhekol, his colleagues in Italy reported Leicester rejected a £20 million offer from the Giallorossi.
Wenger is still considering his options during the start of pre-season, and his hesitancy to sign the player could see the Serie A giants take advantage.
Roma have offered €23 million for Mahrez's signature, per Goal, but this is considered short of the Foxes' valuation of the flair talent.
The 26-year-old appeared 36 times in the Premier League last season, according to WhoScored.com, but Leicester gave up their league title crown with a whimper as coach Claudio Ranieri was dismissed.