"A motion has been filed with the U.S. court seeking the lifting of the temporary restraining order," Keith Oliver, senior partner at London law firm Peters and Peters, told Reuters.
"That has been filed electronically. It has to be signed by the judge and will take effect formally after he signs the document."
GEAR:Save 10% on Liverpool home, away and third kits here, courtesy of Kitbag
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 latest move could 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."
The American pair have also demanded that the club's chairman Martin Broughton and other defendants be jailed for contempt of court.
The Texas case was adjourned on Thursday and was due to resume at 12:00 GMT 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.
NEWS:Liverpool sale clears latest hurdle
NEWS:Liverpool battle returns to High CourtNEWS:Lim withdraws offers to buy Liverpool
NEWS:Hicks and Gillett obtain restraining order
NEWS:
