Nasri's contract expires in 12 months, and there is no sign of the France international putting pen to paper on fresh terms - despite Wenger's desire for him to stay. Chelsea and Manchester United are said to be monitoring the situation, with one eye on poaching the 24-year-old from their rivals.
The Gunners boss also faces the prospect of losing Gael Clichy, who has been heavily linked with Manchester City, as well as skipper Cesc Fabregas, a target for boyhood club Barcelona.
And although Wenger promised to be highly active in the transfer market this summer, he is yet to make a significant purchase, leading to suggestions of disillusionment within the Arsenal squad.
"Money has never been my motivation," Nasri said in the News of the World. "I have always taken decisions from a football point of view.
"I don't want to sign for a club where I wouldn't be playing the football that I like, where I wouldn't feel happy, just for the sake of money.
"We already earn huge wages. The priority is to make a big career and to win titles. This is more important than everything else. I know the value and the meaning of money.
"You have to be able to evolve with a new way of living, keeping respect to my values. Family, friends, a good agent, it all helps you not to get carried away.
"With no titles under your belt, you can't be in the list for the Ballon D'Or. I came to England to get trophies because I haven't won anything in my career, apart from an Under-17 European Championship in 2004.
"We all need to get out of our comfort zone, to grow up and test ourselves. Even without winning trophies, I think I have grown up. I am hungry for titles. I play football because I love this sport and want to feel the emotion of winning. Lifting a trophy all together, this is the beauty and sense of team sports."