The Sunday Mirror says the 24-year-old Gunners captain was head-hunted by Barcelona a year ago, but Wenger persuaded the midfield star to stay.
But if the new European champions come in with an offer of around £40 million, Arsenal will find it difficult to resist.
Fabregas has made no secret of his ambition to return to the club where he started his career, and from where Arsenal signed him as a teenager.
Fabregas has been the first to acknowledge the part Arsenal have played in his development. He admitted after he made his first team debut as a 16-year-old that he would have had no such opportunity had he stayed at the Nou Camp.
Wenger wants to keep the player but accepts that if Fabregas pushes to move back to his native Catalunya, there is little point resisting.