Yes, I have heard this also. When Victoria Station was extended around the 1880s, the area on either side of the River Irk was covered over. That's directly underneath the entrance, where the taxis wait.
It's said that whole houses and streets were buried beneath the station. A cemetery on the banks of the Irk also lies deep underneath Victoria Station, round about where the tram stop is located.
It's said that there are streets and houses below the Cathedral, underneath Victoria Street next to the Irwell.
I think all this may be an urban myth. However one underground street does apparently still exist. That's the underground passageway that used to be the Market Centre. I'm told the entire length of the passageway, once a place to buy jeans, cassettes and other cheap items, is still intact.
There is also a tunnel built in the 1950s which runs from Ardwick to Salford. It's used to carry cables and is not open to the public.
Here are some interesting underground attractions not too far from Manchester: The Stockport Air Raid Shelters
, Hack Green Nuclear Bunker