Mahrez has been linked with a move from the King Power after Leicester failed to secure European football for next season.
The Algeria international has made it clear he wants to join a top club this summer, and bookmakers Betfair have priced Arsenal as 6/4 favourites to sign him.
Premier League champions Chelsea (17/2) and Arsenal's north London rivals Tottenham (14/1) are also in the running for Mahrez's signature.
Mahrez could also make a return to France this summer, with Ligue 1 winners Monaco at odds of 5/2 to become the former Le Havre winger's next club.
Riyad Mahrez wants to leave Leicester this summer
Arsenal favourites to sign Leicester star Riyad Mahrez
The 26-year-old won the PFA Player of the Year having helped the Foxes to a shock Premier League title last term.
And Leicester are in a strong bargaining position having tied Mahrez down to a four-year deal last summer, with reports suggesting they could demand £40million for a player they bought for just £400,000 three years ago.
Mahrez has made no secret of his desire to play in the Champions League every season and released an open letter to the club earlier this week.
His statement said: "I've always enjoyed a good relationship with the chairman and everyone at the club, and I hope I have been able to repay the faith shown to me by my performances and commitment on the pitch during my time here.
Arsenal firm favourites to sign Leicester's Riyad Mahrez this summer How Arsenal could look with Ben Gibson and Riyad Mahrez Sun, May 14, 2017
Is this how Arsenal could line up with Ben Gibson and Riyad Mahrez
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Is this how Arsenal could look with Riyad Mahrez and Middlesbrough Ben Gibson
"I've had the four best seasons of my career at Leicester and have loved every moment. I feel immense pride to have been a part of what we have achieved during my time at the club, culminating in becoming Premier League champions.
"The relationship I share with the club and our amazing fans is something I will treasure forever and I truly hope they will understand and respect my decision.
"I had a good discussion with the chairman last summer and we agreed at that time that I would stay for another year in order to help the club as best as I could following the transition of winning the title and in the Champions League.
"However, I am fiercely ambitious and feel that now is the time to move on to a new experience."