Dunne hasn't kicked a ball since Euro 2012 and was widely tipped over the weekend as a recruit for Thierry Henry's New York Red Bulls.
He is scheduled to return to action in early Februay after a third operation to correct a problem with his hip which first manifested during Euro 2012.
Stephen Ireland is a peripheral figure in Lambert's Villa team but, like Dunne and Given, accounts for a sizeable chunk of the club's weekly wage bill.
Lambert held a transfer summit meeting with chairman Randy Lerner last night.
A a maximum of only around £10 million will be made available to spend in the January window but on condition that some big names must go.
Lambert's position as manager is safe but he is approaching the most critical month of his career and is ready to revise his transfer policy to prevent dropping into the Championship.
Villa have shipped 15 goals in three games over the festive period so far and travel to in-form Swansea tomorrow.