An attorney for Tom Hicks and George Gillett claims the duo are set to drop their £1billion lawsuit.
The American pair were planning to seek $1.6billion in damages following the contentious sale of Liverpool Football Club against their wishes.
John W Henry's New England Sports Ventures took control of the Reds on Friday, put the finishing touches to a £300million deal.
Hicks and Gillett, co-owners at Anfield since 2007, had opposed that deal as the offer fell some way short of their valuation of the club.
However, their efforts to block the bid were scuppered when a High Court ruling sided in favour of their creditors, the Royal Bank of Scotland.
Hicks and Gillett initially refused to accept their fate, though, and took their fight to the courts in the United States, obtaining a restraining order blocking the sale in a Texas court.
They do, however, appear to have now accepted that they are fighting a losing battle and are prepared to drop their damages claim.
Attorney Tom Melsheimer said that Hicks and Gillett were dropping the claim to comply with an English court order, but hinted that the issue may not be over yet with the pair set to take the matter back to the High Court.
He said: "Mr Hicks and Mr Gillett have withdrawn without prejudice their Texas lawsuit in order to fully comply with the order of the English court.
"We believe the order is overbroad and unfair, yet Mr Hicks and Mr Gillett respect the legal process.
"We believe that once the English court finally has a chance to hear all the facts, a very different picture will be painted."
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