The 33-year-old is out of contract at the end of the end of the current campaign, leaving him free to discuss a move elsewhere.
Rosicky has previously stated his desire to extend his near eight-year stint at the Emirates Stadium, even suggesting he could end his career at the London club.
And Wenger has confirmed he wants the Czech to remain at the club, praising the former Borussia Dortmund player's quality.
"Tomas Rosicky will stay here at the end of the season," he said.
"He is a marvellous player and contributes well to the team.
"He is certainly a typical Arsenal player in the way that he is mobile, technically sound and team orientated. He is a fantastic footballer."
Rosicky has made 12 Premier League appearances for the table-toppers this season.
