The Algeria international was heavily linked with a move to the north London side earlier in the summer amid speculation that he could he set to follow N’Golo Kante’s lead and leave the Premier League champions.
Mahrez featured for Leicester as Claudio Ranieri’s men slumped to a disappointing 2-1 Premier League loss at Hull in their first game of the season last weekend.
There have been no fresh reports linking Mahrez with a move to Arsenal in recent days as the Gunners prepare for their trip to the King Power Stadium to take on Leicester City this weekend.
And Mahrez has explained that there are only a select few clubs that he would consider leaving Leicester for.
Speaking in an interview with France Football, Mahrez said: “The Premier League is a super league and I would like to stay here as long as possible.
“Now, there are two or three clubs in the world, that if they come for me, it definitely makes you think, if you understand what I am trying to say.
“I don’t think about it [the speculation] too much. I’m not part of that world. I play football and then I go home.
“It’s true that, in England, they’re crazy about it. Last Sunday, after a game, we were in the same hotel as Chelsea and that was a story. They find the smallest detail to be a part of your life.
“I know how to deal with it. After all, I’m not David Beckham.”
Arsenal lost their opening game of the season 4-3 to Liverpool at The Emirates.
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