Villa boss Alex McLeish confirmed the Republic of Ireland international could be back in contention for the home Barclays Premier League clash with Everton on January 14.
McLeish said: "Shay is not far away and feels he could be ready pretty soon."
He added: "He was champing at the bit over the festive period because he wanted to be involved.
"He could have a chance of being ready for the Everton game."
Given has impressed since his summer move from Manchester City on a five-year contract.
Brad Guzan has deputised for the 35-year-old in his absence.