Funding cuts have left the centre several thousand pounds in debt.
The only asset the committee has is the building, meaning that moving to smaller premises would cut running costs.
The venue is steeped in musical history with hundreds of local bands playing the club.
Yoko Ono, Sir Paul McCartney and Ringo Starr have all contributed to keeping the club open in the past.
Bob Braddock, coordinator for The People's Centre said: "The centre does have considerable debts at present.
"Funding has been quite dramatically cut as it has with a lot of projects.
"Selling the building is one of a number of options which we are considering and will be put forward to the Management Committee in two weeks.
"Our commitment is to our staff and the services that we provide. We are still able to operate and honour all our services and debts at the moment."
Picket manager Philip Hayes said: "On a personal level, I am devastated by the possibility.
"As a Liverpudlian, I am equally concerned about the impact the loss of these cultural facilities and events will have upon the city.
"The Picket has existed for 20 years, putting on gigs for local bands, providing recording facilities and advice for new bands, and benefit concerts for a wide range of community organisations.
"It is difficult for me to accept that, just as we have received the accolade European Capital of Culture and the city appears to be striding forward, our cultural facilities cannot be sustained."
If the committee decide to sell then the site itself could generate them millions.
Property expert Stephen Belin of B.E. In the City Properties said: "I would say that every flat on that site would be worth £40,000.
"This is just speculation because I have not seen the site but My guess, right or wrong, would be that you could probably get 20 in the main building and another 10 in the other part.
"That makes about £1.2m. "But I think you would be likely to get £1.5m to £2m."
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