Nasri is attracting interest from Chelsea, Manchester City and Manchester United and is expected to tell Wenger that he wants to leave Emirates Stadium.
The Gunners have already turned down a £20 million opening offer from United, according to widespread reports, and are eager to keep hold of the French international.
United's offer would represent a fantastic return for a player entering the final year of his contract, but Wenger does not want sell Nasri and is still hoping to persuade the 24-year-old to sign a new deal.
If the former Marseille midfielder rejects a new deal then Arsenal will be hoping City, Chelsea and United enter a bidding war to drive up the price. City distanced themselves from reports last week they had made a £20 million bid, saying there had been no talks between themselves and Arsenal and that, at that stage, none were planned.
They have, however, just signed Nasri's team-mate Gael Clichy for £7 million and need to reconsider their transfer targets after missing out on Udinese midfielder Alexis Sanchez.
Chelsea's primary target this summer has been Tottenham Hotspur midfielder Luka Modric, but Spurs have steadfastly refused to entertain any offers for their Croatia international and Nasri represents a viable alternative.