Multi-millionaire McCartney, who owns the Liverpool Institute of Performing Arts (LIPA) situated next door, will try to stop the landmark college from being demolished or made into appartments.
The Institute's co-founder Mark Featherstone-witty, says, "It would be poetic if LIPA, which is on the site of Paul's old school, and the building that was John's old art college were joined together.
"We are looking to expand, so it has come at a good time for us. I would like to see the buildings preserved for artistic purposes."
A spokesman for local tour company Cavern City Tour's Magical Mystery Bus Trip says, "That building is synonymous with The Beatles. It's where John and (his first wife) Cynthia met and there's a fantastic photo of the two sitting on the steps outside.
"Paul and GEORGE (HARRISON) were at the grammar school next door. They used to jump over the adjoining wall into the art college to visit their mates."