Melanie Brown, also known as Mel B, was hoping to take her daughter, a result of a short-lived relationship with the Hollywood star in 2006, with her to host the Australian X Factor show for the third year running.
However, it has been reported Mr Murphy refused to sign a parental consent form to allow his daughter to travel to Australia for a sustained period of time.
A spokesperson for the X Factor's network, Network 7, said Ms Brown is fighting custody battles with more than one of her children’s' fathers.
"[Ms Brown is] fighting custody battles in LA and London. It's looking increasingly likely Mel will have to live and work in LA," said Brad Lyons, Seven's director of production, adding that the show might have to make do without the lively judge.
"She was a very good judge. That's why we exercised the option to have her return. She is outspoken and a big international star."
Seven's production lawyer, Jane Oswald, has said the problem has been Mr Murphy's reluctance to sign to required documents.
"Eddie Murphy wouldn't sign the documents," said Ms Oswald. "[He said] they would have to take him to court to get the documents signed."
Mr Lyons said the company was already working a solution to include Ms Brown on the show, such as flying her in and out as needed, but that he would not 'tear her away from her kids'.