A club spokeswoman could not confirm what appeared to be a last-ditch attempt to hang on to the club by the American pair, whose representatives could not be immediately contacted.
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The BBC said the move seemed designed to help Hicks sell his stake to U.S. hedge fund Mill Financial rather than enabling NESV, who own Major League Baseball's Boston Red Sox, to complete their deal.
Liverpool, the five-times European champions who are one of England's greatest clubs and possess a brand of global stature, have been caught in a bitter ownership battle that has overshadowed their troubled start to the season.
The club's board have agreed a 300 million pound deal with NESV, whose owner John W Henry dismissed the latest move by his rivals.
"We have a binding contract," Henry said on his Twitter feed. "Will fight Mill Hicks Gillett attempt to keep club today. Their last desperate attempt to entrench their regime."
Hicks and Gillett, who face a Friday deadline for the repayment of 200 million pounds of debts to Royal Bank of Scotland (RBS), believe the sale undervalues the club and have described it as an "epic swindle."
An RBS spokesman said on Friday he had heard reports of the injunction being dropped but had no direct knowledge of it.
Hicks and Gillett were granted a temporary restraining order on Wednesday by a Texas court, pouring cold water on euphoric fans who had been celebrating a High Court ruling that the owners could not block the sale by sacking board members.
The American pair have also demanded that the club's chairman Martin Broughton and other defendants be jailed for contempt of court.
That case was adjourned on Thursday and was due to resume at 12:00GMT Friday - three hours before the British High Court's deadline for the American duo to comply with their ruling.
Failure to meet the Friday deadline for repayment of debt could see Liverpool put into administration and docked nine points in the league.
However RBS is considered more likely to extend the loans to Monday given the fact that there is a buyer waiting for the go-ahead.
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