Mahrez is on the verge of turning down a bumper £100,000-a-week deal to remain at the Premier League champions, which has put Chelsea on red alert.
But bookmakers SkyBet have placed Arsenal as 7/2 favourites to sign Mahrez, who has been linked with a move to the Emirates Stadium since last summer.
Chelsea have been priced at 5/1 to land Mahrez before the summer window slams shut, while the 25-year-old can be found at 1/1 to remain at the Foxes.
Mahrez, who cost Leicester just £400k in January 2014 from Le Havre, scored 17 goals and assisted 10 last season to help guide the Foxes to the Premier League title.
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Arsenal ahead of Chelsea in Riyad Mahrez pursuit
Leicester boss Claudio Ranieri is seemingly confident last season's PFA player of the year will remain at the King Power Stadium next term.
"I am very confident with him. He stays here with us," the Italian boss said. "He enjoys it and is not a man saying 'coach I want to go'. He is happy."
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