The Gunners will not be looking to bring their former captain back to the Emirates Stadium, opening the door for their Premier League rivals to sign the Barcelona midfielder
Chelsea and Manchester City have tabled £28.4 million bids for Cesc Fabregas, Goal understands.
The Premier League big-hitters have made identical moves for the Barcelona midfielder and now appear to be locked in a straight fight to sign him this summer.
Chelsea manager Jose Mourinho admitted on Thursday that his club were closely monitoring the situation of Fabregas, who has been told he can leave the Nou Camp this summer.
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City also want to lure the 27-year-old back to the Premier League and have followed up their interest with a formal move amid growing uncertainty at the club over the future of Yaya Toure, who has made it clear he is not entirely happy at Etihad Stadium.
But Arsenal have rejected the opportunity to match Chelsea and City's bids, and will not be re-signing their former captain this summer.
Under the terms of the buy-back clause in Fabregas' Barcelona contract, the Catalan club had to inform Arsenal of any bid for the player and give them the opportunity to match it.
Manager Arsene Wenger was keen on a reunion with Fabregas but does not want to pay more than £25m for the player.
Arsenal are in the market for a £30m-plus attacker this summer and, given the squad overhaul that is expected to take place, are reluctant to spend more than £60m on just two players.
Mourinho went public with his interest in Fabregas when speaking at a Yahoo event in Belgium on Thursday.
"I think he is eager to leave Barcelona and very motivated by the idea of returning to England. I think that is pretty clear.
"After that, whether he signs for us or someone else is not a question for today, tomorrow or before the World Cup. We are interested to see how the situation evolves."
Chelsea are in the market for a central midfielder after agreeing to sell David Luiz to Paris Saint-Germain for an initial £40m and releasing Frank Lampard.
Goal revealed in April that Barcelona would listen to offers for Fabregas this summer as they looked to free up funds to reshape their midfield.
Barca and their new manager Luis Enrique are looking to sign Atletico Madrid midfielder Koke and have told Fabregas he can find a new club.
The Barca academy graduate is at a crossroads in his career as he enters the final two years of his contract with the Catalan club in July.
Fabregas was jeered by home supporters during Barcelona's 2-1 home victory over Athletic Bilbao in April and became a scapegoat for fans towards the end of last season.