Dunne, 33, has been sidelined since last summer's European Championships by hip and groin problems and he has had three operations.
His current deal ends this summer and Villa manager Paul Lambert said: "It is not a case of running out of time.
"I know what the guy can do. It is not as if he is 19 or 20 years old and has to impress.
"I have an open mind but the main thing for me is that he is going to be fit again."