The Czech playmaker stood in for Mesut Ozil, who was carrying a thigh injury, against Sunderland and was instrumental in the Gunners' 4-1 victory at the Emirates Stadium, where he scored a well-executed third goal.
Rosicky joined Arsenal from Borussia Dortmund in 2006, but has seen his time in London hampered by a string of injuries.
The creative midfielder is out of contract in the summer and will turn 34 in October, but Wenger revealed a deal for an extension was close to being announced.
"Tomas Rosicky will stay
We have an agreement with him and it will come out soon," the Arsenal boss said.
"I am absolutely adamant he has to stay at the club."
Wenger was impressed with Rosicky's contribution to what was an accomplished display on the back of the disappointing midweek Champions League defeat to Bayern Munich.
"He is maybe one of the players who plays the game of give and move, is a great accelerator of the game," Wenger said.
"When the ball comes to him it is 'boof'
It is second gear now and that is something I admire in him.
"He makes always things happen, not with individual dribbling but with individual acceleration of his passing and of his runs."
Wenger added: "When he arrived here he was less a tactical player and more the 'Mozart from Prague' and he was purely creative, offensive player.
"Today he is a real organiser on the pitch as well
I like to have him in the team because he gives a real structure to our team."
Source : PA