The closure follows raids by trading standards and police who seized pirate DVDs and CDs.
Kitgrove spokesman Hugh Stallard said: “Due to allegations by Liverpool council the market will be closed until further notice.”
A council spokesman said: “We have not yet received notification from Kitgrove about their intention to withdraw from the market.
“However we have written to site owners and market operators recently, warning them that if they allowed criminal activity to continue at the market they would be liable to prosecution.
“This follows a number of raids in the last six months when millions of pounds worth of counterfeit and pirate goods were confiscated.”
The market, based at Stanley Dock, is owned by Kitgrove but run by a specialist operator and licensed by the council.
Counterfeiting costs the entertainment industry an estimated £77m a year.
Last year the ECHO revealed how fake DVDs produced for less than 50p each sell for up to £5 on Merseyside market stalls.
The Heritage market owners have dubbed the business “the Camden of the north”. It sells a range of goods including clothing, household goods, furniture and jewellery.
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