John Robertson is the first major MP to back the scheme, which would see shipbuilding on the Clyde secure "for much of the rest of the century".
He said: "The down side would be the closure of Govan, although it would pick up work from Scotstoun while it was being renovated."
BAE Systems, which runs both yards, entered formal planning consultations on two options for building a new generation of frigates, Type 26, for the MoD.
Mr Robertson said: "Firstly, both Govan and Scotstoun could stay open.
"Or, secondly, we could set up the Clyde to be a state-of-the-art shipyard.
"My favoured option is to spend hundreds of millions of pounds at Scotstoun and secure shipbuilding in Scotland for much of the rest of the century."
Current orders for smaller patrol vessels would be carried out at Govan.