Vieira called time on his playing career last week to take up an off-field role with Manchester City as the club's new Football Development Executive, having guided the Gunners to three Premier League and four FA Cup titles during his nine-year stay at Highbury.
And 25-year-old Vermaelen hopes that one day his name can be heralded alongside the great Frenchman.
"What Patrick Vieira did for Arsenal was amazing. Every player, especially me, dreams of that, to be a legend for the club," he said in The Sun.
"Maybe I can be the captain one day, it's up to the boss."
The centre-back enjoyed a successful debut season in Arsenal's colours after arriving from Ajax for £10 million in summer 2009, scoring eight times in 45 appearances.
However, Vermaelen made just five outings for the Gunners last term in an injury-wrecked campaign, and he is now hoping that his long-awaited return will signal the arrival of silverware for the club for the first time since 2005.
"Last year we came so close. Four or five weeks before the end we were still fighting for the title.
"I was injured and I was thinking we were winning this title. I believe in this team, in how we play. We can win things. We're really close."
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