A hearing to discuss the restraining order brought on behalf of Liverpool's parent company Kop Investment, owned by Hicks and Gillett, and the contempt motion was adjourned after 90 minutes and will resume on Friday at 12:00 GMT, a court official said.
The 160th Civil District Court in Dallas on Wednesday had issued a temporary restraining order on Broughton, the Royal Bank of Scotland, which is the club's largest creditor, and prospective purchasers New England Sports Ventures (NESV).
Earlier on Thursday in London, a High Court judge granted an injunction to restrain the Dallas court ruling, saying the case had no connection to Texas.
The judge said his ruling was not aimed at the Dallas court but at Hicks and Gillett and gave the duo until 15:00 GMT on Friday to comply with his orders.
NESV, which owns the Boston Red Sox, had an offer to buy the English Premier League club for 300 million pounds accepted by Liverpool's independent directors but Hicks and Gillett have fiercely contested the proposed deal.
Asked when he expected the sale of the Merseyside club to go ahead, Broughton told Sky Sports News: "I think probably sometime tomorrow. We're nearly there. We'll have to see, we've still got to take away the restraining order."
In the motion for contempt filed in Dallas and seen by Reuters, lawyers for Hicks and Gillett said:
"Further showing their unlawful intentions and brazen disgegard for their obligations, Defendants have undisputedly and according to their statements, quite proudly, violated this Court's temporary restraining order".
The motion, which was not the main point of discussion at Thursday's hearing, asked for the "incarceration of Defendants until they cure themselves of contempt and fine the Defendants for their actions."
The motion also requested a daily fine of $50,000 be imposed until the contempt of court was ended.
