Villa are poised to replace one veteran in Brad Friedel with another in 35-year-old Given who wants the chance to play first-team football again.
The two clubs have held talks and sources close to Villa are optimistic a deal will be finalised sooner rather than later.
Given was the number one at Newcastle for more than a decade before moving to Eastlands two and a half years ago.
But the emergence of England keeper Joe Hart - who played under McLeish when on loan at Birmingham - cost him his place last season.
Personal terms are not expected to be a major stumbling block even though Given is reported to be on ?£80,000 a week at City.
The expected arrival of Given, however, will not lead to the departure of Brad Guzan who had a spell on loan at Hull last season.
McLeish is keen for the American to provide back-up to Given along with Andy Marshall.
He said: "I'd like to hold onto Brad, definitely. I don't think we will be letting him go at this particular stage."
Source: PA
Source: PA