Merseytravel's plans include the possibility of building a second storey on car parks at Bromborough, Green Lane, Hooton and the under-construction Liverpool South Parkway.
Mr Cook added: "Park-and-ride is only part of the solution. We have to get more commuters out of their cars and on to public transport for their whole journey.
"On Saturdays, between 70% and 80% of city centre visitors come in on public transport."
University to help with more spaces
MERSEYTRAVEL'S plan was revealed at a meeting of the council's car parking panel.
Councillors were also told that the University of Liverpool is willing to open up its car parks to evening and weekend visitors to ease city centre parking problems.