N'Zonzi doesn’t fancy championship football so he wants to leave the club so that he can remain in the Premier League.
Stoke, Chelsea and Sunderland have all been linked, so had the Gunners earlier on, now it seems they are ready to act.
Initially, Rovers valued the player in the region of £10million, but that figure now seems unlikely and they may have to take around half of that, the player has also been left out of the squad that takes a pre-season tour of Austria.
Manager Steve Kean said in a statement: "Steven has asked for a transfer. We want players who want to be here so he was left at home.
"He's made it clear he wants to play his football elsewhere so we'll be listening to offers.
"At the moment, we are not planning to have him in the squad. He's not taken part in any first-team sessions."