Rosicky scored his first goals of the season on Saturday in the Gunners' 2-1 win over West Brom and afterwards Wenger spoke of his admiration for the 32-year-old.
The Czech Republic star's time with the Gunners has been plagued by injury and form struggles, but his manager believes his double scoring performance against the Baggies illustrated his worth to the club.
Wenger is convinced Rosicky still has an important role to play for the north Londoners in the future despite speculation that he could quit in the summer following a Premier League campaign which has seen him play just five times, including yesterday's outing against Albion.
The Frenchman 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."