The Daily Mail says the Catalans are desperate to reduce the prohibitive £80million demanded by the Gunners for their captain and are considering several players to offer in part-exchange.
Arsene Wenger would be keen on midfielder Yaya Toure if he is to lose Fabregas, but the Ivory Coast midfielder is holding out for better offers.
The Emirates boss is also not keen on a straight swap for Sweden striker Zlatan Ibrahimovic, but throwing Hleb into the mix could give the Frenchman something to think about.
The 29-year-old did not leave north London in the best of circumstances two years ago, but admitted last summer that he should never have left the Barclays Premier League.
"For me, Wenger was like a father. I consider him one of the best managers in the world," he said last July.
"For such a boss one wants to die on the pitch. Arsene managed to create a smashing team with a wonderful atmosphere inside of it."