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Mahrez, 26, helped Leicester beat odds of 5000/1 to win the Premier League in 2016 but now he wants out.
He announced in May that he is desperate to leave the club and the Foxes are holding out for a big transfer fee.
Arsenal and Roma have both been linked with a move for the Algerian and former Sky Sportsman Keys, who now works for BeIN Sports, thinks he’ll end up at the Emirates.
He was asked on Twitter: “Richard, where do you think Mahrez will be next year? Leicester? Roma? Spurs? Or Arsenal? Thanks.”
Keys responded: “I still believe Arsenal.”
Boss Craig Shakespheare today confirmed the club had rejected a bid from Roma for the winger.
“The bid was politely declined because it was a low offer,” said Shakespeare.
“I don’t know what it was and I don’t get involved.”
Mahrez, who is valued at £50million, made 48 appearances for Leicester last season.