I work in the area and as far as I know there is no longer a place called Albert Square in the Old Trafford area.
On the One Show last year he said that he lived on Queens Square which backed onto Loretto College. Much of this area was demolished in the late 60's / early 70's there now stands a set of tower blocks (some of which the local housing association is planning to demolish in the next year or so).
The college is still there - there is a nearby street called St Mary's (the name of Morrissey's old school).
This area is about 2 miles away from where the football club is based (which isn't actually in Old Trafford, more like Gorse Hill).
Dave