The Belgium international was previously linked with a move away from the Emirates due to his lack of first-team football.
West Ham United have only recently emerged as potential suitors for the centre-back, whose contract expires in 2015.
However, Wenger has insisted that he is not prepared to let go of the 28-year-old, who has been an Arsenal player since 2009.
According to the club's official Twitter page, in this morning's press conference Wenger said: "I'm ready to extend Vermaelen's contract. He is a quality player and I'm open to it."
Wenger has also claimed that the North London outfit are "unlikely" to sign any new players this month.