Hi Tony,
Unfortunately due to space restrictions there is no car parking at the port. There are a variety of car parks in Liverpool with the following two being rather close to the port:
Liverpool Q Park - 0151 232 2150
www.q-park.co.uk/parking/parkingid/582
Capital Car Park - 0151 707 2666
www.ukcarparks.info/the-capital-car-park-car-park-liverpool
http://www.steam-packet.com/ourports/Liverpool which provides information on their preferred car parking partner along with a link and code to save 10% if you book online with Q-Park.
I hope this information helps.
Kindest regards,
Julia