According to the newspaper, the woman – who has not been named – claims she gave birth to the rockstar’s daughter last year after they had a one-night stand together.
The publication reported that the mystery woman is suing him in a New York court for £2million.
It is alleged the woman is willing to take DNA tests to prove her case and that she wants the 40 year-old rocker to pay paternity costs.
It has also been reported that the case's first hearing last Friday was adjourned until later this month.
A spokesman for the former Oasis frontman refused to comment on the story but confirmed that his lawyers are taking legal action against the New York Post for reporting the claims.
The spokesman told a UK newspaper: 'Lawyers are taking action against the New York Post. We are not going to comment on gossip.'
The 40 year-old rocker, who is currently married to All Saints singer Nicole Appleton, already has three children.
His first child Molly was conceived during an affair with Lisa Moorish in June 1997, just a couple of months after he married Patsy Kensit.
Liam went on to have a son, Lennon Francis Gallagher, with Patsy in 1999 later before the couple divorced a year later. Liam’s second son, Gene Gallagher, was born to wife Nicole in 2001.