The 24-year-old Familiar hitmaker reportedly enjoyed a date with the 18-year-old brunette beauty at London’s lavish Bulgari Hotel last week.
Last month, they were also pictured at the same Dolce & Gabbana event, a star-studded fall in Lake Como.
Reports of their romance come six weeks after he announced his split from Cheryl, 35, with whom he shares one-year-old son Bear.
A source told The Sun: “Liam and Maya get on well — and she’s a stunning girl.
“They have kissed a couple of times, but he is in no rush to date again and certainly isn’t ready for a serious relationship.
“Liam is simply focusing on work at the moment, and above all else obviously his main priority is Bear,” the insider added.
Liam was first pictured with Maya at a meet and greet event with One Direction when she was 15-years-old.
They are said to have been introduced by Maya’s model brother Thomas, 18.
A source also told the publication: “Liam gets on really well with Thomas and Maya, and all of their gang.
“But he’s too savvy by now to follow Maya on social media, as he knows he will be linked to any girl he does.
“He enjoys hanging out with the family because they’re a great bunch and, clearly, have no interest in his money or fame,” they said.
Express.co.uk has contacted representatives for Liam and Maya asking for comment.
Maya is the daughter of Texan multi-millionaire Thomas J. Henry, who is a high-profile lawyer and runs a personal injury law firm in the US.
Maya is also a keen tennis player and aspiring human rights lawyer.
Recently, she moved into modelling and has already opened a show for D&G in Mexico and featured in Elle Czech.
Cheryl and Liam confirmed their decision to split on July 1, with the father-of-one telling his 32 million Twitter followers: “Cheryl and I are sad to announce that we are going our separate ways.
“It’s been a tough decision for us to make. We still have so much love for each other as a family.
“Bear is our world and we ask that you respect his privacy as we navigate our way through this together,” the statement said.
A few weeks later, he was snapped looking cheerful as he left a London hotspot with two female companions.
Liam reportedly left in the early hours after dinner with the unknown pair.