The 33-year-old has yet to make a single appearance this season having undergone surgery numerous times, but the Scot remains keen for him to pen a new contract
The Republic of Ireland international, who has yet to play a game this season following a lengthy battle with injury, will be a free agent upon the expiry of his current deal in the summer.
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"It is not a case of running out of time," Lambert told reporters when asked about Dunne’s contract. "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."
Dunne travelled to Philadelphia last week to visit the surgeon who carried out his third operation, and Lambert is confident the centre-back's recovery will run smoothly.
“We will have to wait and see what the surgeon has said about the injury," he continued.
"I am pretty sure that he will not require another operation. The advice that Richard has been given is that he will just have to battle through the problem.
"I will have rough idea of what will happen after what the surgeon has been saying to Richard. The surgeon expected this to happen and the advice was to go back and see him again if it did.
"First and foremost the main thing is to get the guy back to fitness. That is the big thing for me. There is nothing in my mind other than getting that lad fit."