The British actor has revealed he's in negotiations over the role with filmmaker Joss Whedon and executives at Marvel.
He tells Collider.com, "I feel really flattered and honoured that they came to me for that role... I think he's (Quicksilver) an interesting character and we're just gonna keep going into that.
"I sat down with Joss, I think he's awesome, I sat down with the guys at Marvel and they're also great; I think it'd be interesting."
In the Marvel universe, Quicksilver is the lightning-fast mutant twin brother of the Scarlet Witch.
It is still not clear who will be appearing in The Avengers sequel, titled Age of Ultron, apart from Robert Downey, Jr, who confirmed he'd be returning as Tony Stark/Iron Man last month (Jun13).