If the motion is passed, chief executive Colin Hilton will be tasked with drawing up a report examining various locations.
It is hoped the project would be completed by next May, the 40th anniversary of the release of the Beatles’ final album, Let It Be.
In the run-up to the Capital of Culture year, some were keen to stress Liverpool had more to offer than just The Beatles.
But Cllr Clucas said she believed there was more to be made of Liverpool’s Beatles history.
She added: “From my point of view, The Beatles are big business, whatever you think about their music – which I happen to love.
“Look at the classic performers like Elvis Presley, and Graceland, his home in Memphis – their home towns exploit it to the full.”
She added the lure of The Beatles could not be underestimated in terms of its economic value to the city and the wider promotion of Liverpool outside its boundaries.”
