Wenger, who takes charge of his 1,000th game as Gunners boss when they travel to play Chelsea on Saturday, has admitted that he would like to sign an extension to his current deal, which runs out at the end of the season.
Speaking before the clash at Stamford Bridge, Vermaelen said that "everybody" wants to see Wenger sign on the dotted line.
"Everybody wants him to stay as long as he can. He's been incredible with what he's done for this club and for the players as well," Vermaelen told Sky Sports News.
"We would be really happy to see him signing on for a few more years. If you see him off the pitch there's always a lot of hunger in him and a lot of ambition still. He's not losing that at all."
Wenger, who joined the Gunners in 1996, has led the club to three league titles and four FA Cup successes.