The 31-year-old Spaniard's legal representatives are now in advanced talks with LIV over a potential agreement to end his association with the league.
Rahm's lawyer, John Beck, told the hearing that his client had "independently reviewed the terms of LIV 2.0 and determined those terms are unacceptable as to him" - although it's not clear what the terms are.
It was later confirmed that LIV and Rahm's representatives are "in advanced discussions for a consensual separation agreement between Mr Rahm and LIV".
The agreement is hoped to be finalised by a court hearing on 5 November.
LIV filed for Chapter 11 bankruptcy protection in the United States in September after Saudi Arabia withdrew its multibillion-dollar funding. The league has since secured a possible $300m in financing from BC Partners Credit as it seeks to continue into the 2027 season.
LIV's players are owed at least $45m and have the option to leave the league, with an extension now allowing LIV to continue discussions with its players until 25 October.
Court documents listing the 30 largest unsecured claims show that Rahm is owed $7.5m, the largest amount owed to any LIV creditor.
Chapter 11 bankruptcy protection allows a US company to postpone its obligations to creditors while it reorganises its debts or sells parts of the business.
Saudi Arabia's Public Investment Fund (PIF) is providing $49.6m in financing to help fund the bankruptcy process.
LIV insiders remain positive about the league's future, saying talks with players are progressing and that the statements made in court have not changed the momentum behind the proposed transaction.
Louis Oosthuizen has confirmed he will not re-sign with LIV Golf, opting to return to the DP World Tour in January 2027 in what he describes as the hardest decision of his professional career.
LIV Golf has accused the DP World Tour of interfering with its restructuring plans after the European circuit announced that players who join the breakaway league next season will be denied membership.
Rory McIlroy feels that the LIV Golf concept was originally a good idea that was "executed poorly" as the breakaway tries to relaunch after filing for bankruptcy.
The DP World Tour has announced it will not grant membership for the 2027 season to any player who joins LIV Golf next year.
