Wenger is out of contract at the end of the campaign having signed a new deal in August 2010 and there are doubts surrounding the Frenchman's future in London after 18 years in the top job.
The 64-year-old, Arsenal's longest-serving manager, was tipped to put pen to paper on a new contract in March but the club's crushing 6-0 defeat to London rivals Chelsea last month, which saw them slip seven points off the pace, has led to suggestions he may quit.
Arsenal have reportedly made contingency plans in the scenario Wenger departs the club, with Diego Simeone of Atletico Madrid, Borussia Dortmund's Jurgen Klopp and Everton manager Roberto Martinez among the contenders.
However, Vermaelen insists Wenger has the support of the entire dressing room despite Arsenal's nine-year drought without silverware.
"Everybody wants him to stay as long as he can," the Belgian international said.
"He's been incredible what he's done for this club and for the players as well. We would be really happy for him signing on for a few more years.
"The spirit is unbelievable in the team. We've worked a lot on our team shape and everybody knows their role in the team, everybody’s working for each other and that’s because there is a great team spirit. That’s the great improvement for us this season.
"It is just the hunger in the team. Of course it was there before but the spirit is great and you can see us fighting for each other really hard."
After leading the Premier League for most of the season, Arsenal have dropped to fourth in the table behind pacesetters Liverpool, Chelsea and Manchester City.
Arsenal, however, remain in the hunt for the FA Cup trophy. The 10-time winners face defending champions Wigan Athletic in the semi-finals at Wembley Stadium on April 12.
