The Oasis singer has never met the baby he fathered with U.S. journalist Liza Ghorbabni.
And despite repeated demands for him to attend a hearing in New York to discuss maintenance for his daughter Gemma, now 21 months old, he has so far refused and has already been fined $5,000.
Now Liza's lawyer, Ira Garr, said the singer will get fined again for his failure to make a deal.
And Liza's father Danny spoke for the first time to condemn Liam for 'dodging' US justice by failing to attend the last hearing because he was apparently ill – for which he was fined $5,000.
Mr Garr told the Mail: "I assume he will come over. The judge will sanction him again if he doesn't come. To not come over would be foolish."
The lawyer added that he believed a deal was not far off and hoped it would emerge in the coming months.
All that remains are 'nitpicking issues' like how to ensure Liam pays and what to do if he stops paying.
But he said the main problem 'seems to be the accountants'.
Explaining why there was no deal with the rock star, he said: "It might be for want of a lack of a better word, a lack of focus.
"If you have lengthy financial matters in if there's a child support case it's far more taxing than the child support issue which is basically coming to a number and how it's going to be paid."
Liam, 42, had Gemma with Liza, 40, in 2013 after she interviewed him for the New York Times.
Since then the two have been battling it out in the courts about child support.
Liza had filed a $3 million lawsuit against Liam at the Manhattan Family Court but after the case was dismissed she refiled in the Manhattan Supreme Court.
Gallagher is currently paying her $5,000 a month until a final decision about child maintenance can be agreed.
Mr Garr said that unless a deal is reached then the monthly payment could be reviewed every three years, and Liam could end up being the loser.
New York child custody laws state that Gallagher could be forced to pay more if his income goes up by 15 per cent in that time, not to mention the inconvenience of regular renegotiation.
Mr Garr told the newspaper: "Liam's band [Oasis] has disbanded. Let's say he and his brother work it out and get back together.
"If they did do they would make a zillion dollars. When [bands] don't perform in years and they go back on tour they make a fortune.
"Why would someone subject themselves to coming back [to New York] every three years?
"When you do an agreement it's done. That's it."