The Gunners are looking for defensive reinforcements before the transfer window closes, with Flamengo's Pablo Mari their prime target.
But Parlour believes the Premier League proven Dunk would be a worthy signing.
"I like the way he plays, I think he's a proper centre-back. That's what you need sometimes.
"Sol Campbell was a proper centre-back, he was a stopper. He would stop you scoring and that's what you want from your centre-back, they don't need to be great on the ball.
"Someone like Lewis Dunk, who probably is a little bit unlucky not to be more in the England squads."