The Daily Star says Wenger is desperate for Nasri to commit his future to the Gunners after contract talks stalled over his pay demands.
Nasri has one year left on his current deal with Arsenal but has so far stunned the club with his huge wage demands.
He wants a new deal worth £6m a year - which is more than skipper and star player Cesc Fabregas is on.
The Gunners have refused to meet the demands and Nasri has been linked with a shock summer move to Manchester United.
They plan to stand firm over a new contract, with Wenger hoping a compromise can be reached.