The Irishman sustained the injury while on international duty but Paul Lambert has stated that he will not seek compensation from the Football Association of Ireland
The 33-year old had his third operation on Thursday to try and resolve the groin and hip injury that occurred at the European championships.
It is likely that Dunne will miss Ireland's games with Sweden and Austria in the New Year.
"Richard has had the operation in America and we are all hoping that once and for all it will be cleared up," Lambert told the Irish Examiner .
"This was the only place where we could get it done.
"He will come back over from the States in the next few days and hopefully start his rehab and then begin to look to the future.
"I’ve never seen anything like this and the medical people have never seen anything like this either. We have got to hope it has now been cleared up by this operation.
"The original injury occurred at the Euros and sometimes you can get to the bottom of it quickly and on other occasions it takes longer than you think.
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Lambert confirmed Villa were not seeking compensation and added: "We have not been down that road. Injuries can happen to players."
Despite a 3-1 win over Liverpool last time out, the Villans face a defensive crisis with first-team players in short supply.
Villa sold James Collins to West Ham and sent Stephen Warnock and Alan Hutton out on loan, while new signing Ron Vlaar is sidelined with a calf problem giving Lambert a selection headache ahead of their game against Chelsea.