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 amongst the best in the world.
However, any transfer could hinge on whether Arsenal can tie up a deal for Monaco's Thomas Lemar.
Arsene Wenger is a keen admirer of the 21-year-old and has already tabled a bid of €35 million – which was rejected – for the youngster.
Monaco are desperate to hold on to some of their stars given Bernardo Silva has already been sold, while Tiemoue Bakayoko is on the verge of signing for Chelsea, and Benjamin Mendy and Kylian Mbappe both subject to major transfer speculation.
Roma's opening offer of €23m could also be a sticking point, but the club are likely to raise their bid to closer match Leicester's valuation of the 26-year-old if Arsenal do not come calling.