The north London club have gone six years without a trophy, and the Frenchman has been linked with a move away to rivals Manchester United - who are now the most successful club in England.
For his part, the 23-year-old has refused to confirm whether or not he intends to remain at Ashburton Grove.
"We will do everything to keep Nasri at the club. My wish is that he stays here," Wenger said, according to The Sun.
"If he looks back he can see that he's come quite a long way with us, and I think there is still a bit to do. It's the club that makes the player's career."
The Gunners skipper Cesc Fabregas has also been linked with a move away from the club, with Barcelona having been interested in signing him in the past.
"I will be pretty clear about this. For me, Fabregas is with Arsenal for a long time and he will stay with Arsenal," said Wenger.
"It sometimes happens that the rumour can make the transfer.
"Next year will see the introduction of the financial fair play system, which will limit the big transfers.
"I think this is the last year that the summer will be hot - very hot."
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