The unidentified plaintiff, who is a celebrity journalist in her 30s, said she became pregnant during an affair with Gallagher and gave birth to their daughter less than a year ago.
The Post said Gallagher's response to the lawsuit filed in Manhattan Family Court wasn't immediately known and the case has been adjourned until later this month.
Gallagher, 40, is known as the former lead singer of Oasis and the current front man for Beady Eye. He has been married to Canadian singer and actress Nicole Appleton since 2008 and is already the father of three children.
Beyonce flaunts bikini body, Blue Ivy in vacation pics
Kate Middleton recycles dress at movie premiere