The `Taken 2` actor - whose wife Natasha Richardson tragically died in a skiing accident in 2009 - reportedly called time on his two-year relationship with PR executive Freya St Johnston in order to focus on work and his two sons.
A source told the Mail On Sunday newspaper: "Liam is heading back to America at the start of next month to work on his new film `Non-Stop`.
"He told Freya that he wants to take a break and concentrate on his family."
Liam recently revealed he is considering becoming a Muslim after falling in love with the religion and its rituals during a trip to Istanbul in Turkey.
He explained: "The Call to Prayer happens five times a day and for the first week it drives you crazy, and then it just gets into your spirit and it`s the most beautiful, beautiful thing.
"There are 4,000 mosques in the city. Some are just stunning and it really makes me think about becoming a Muslim.
"I was reared a Catholic but I think every day we ask ourselves, not consciously, what are we doing on this planet? What`s it all about?
"I`m constantly reading books on God or the absence of God and atheism."