After Rosicky, 32, scored both goals in the 2-1 win at West Brom to lift the Gunners into fourth spot, Wenger said he hoped the midfielder would stay put.
The Arsenal boss said: "I thought he was fantastic - he's not a player I want to lose. I rate him very highly.
"He has one year left on his contract but I hope he stays and finishes his career with us here.
"He's had a difficult season and been injured.
"But he always seems to come in and gives us a lift at the end of the season. He's a quality player."