Wenger, 64, takes charge of Arsenal for the 1,000th time on Saturday when they travel to leaders Chelsea as they bid to close the gap on Jose Mourinho's side to one point with a win.
The match could be the last time Wenger takes Arsenal to Stamford Bridge with his contract expiring at the end of the campaign, but Vermaelen said the squad were keen to continue working with the Frenchman.
"It's incredible - not a lot of managers do that nowadays because they come in and out, so for him to achieve 1,000 games is something unbelievable," the Belgium defender told Arsenal.com.
"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 has found himself on the bench for long periods of the season due to the form of Per Mertesacker and Laurent Koscielny but he bears no ill will towards Wenger, who is expected to stay on.
"We would be really happy to see him signing on for a few more years," Vermaelen said, adding that there was no sign of him slowing down.
"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."
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