The Frenchman has come in for some criticism with Arsenal having not won a trophy for nine years, but only Hull City stand in the way of an 11th FA Cup win.
And club captain Vermaelen believes doubts about Wenger's leadership could prove to be a driving force for the London club.
"Everybody will do it for him, for the players and for the fans," he said. "I said there has been a lot of talking about us not winning for a long time and we are doing it together for the whole club and for him as well.
"It would be a massive boost if we could win it for the next few years as well.
"There is loads of potential in this team and a lot of good players, so it would give them confidence for the following years.
"Hull is a good team and have a great manager. The final is always something special, so it doesn't mean we are going to win easily."
The London club face Steve Bruce's side in the Wembley showpiece on Saturday.
