Liam Neeson isn’t one to kiss and tell. The Irish actor revealed in a recent interview that he’s currently dating an “incredibly famous” woman, but declined to name his new love, leaving fans to speculate.

When asked by the Irish Independent whether he has a special lady in his life these days, the Taken star replied, “Yes, but I’d embarrass her if I said her name, she’s incredibly famous. I’ll have to do my best for her. It’s amazing how far a simple bunch of freshly picked flowers will go in a lady’s life, I find.”

Fans have guessed several Hollywood leading ladies online via Twitter, with names ranging from Halle Berry to Demi Moore to Dame Judi Dench.

Neeson, 63, has kept his personal life largely out of the spotlight in the years since his late wife Natasha Richardson’s untimely death in 2009. Richardson, whom he met on the set of a production of Anna Christie, died of brain injuries after a tragic skiing accident in Canada. She was 45.

The pair had two kids together, sons Micheál, 20, and Daniel, 19. (Neeson’s older son, Micheál, costarred with him in a Super Bowl 50 ad for LG that aired on Sunday, February 7.)

Last month, the actor opened up to SiriusXM’s My Favorite Song with John Benjamin Hickey, sharing a sweet anecdote from his 1994 wedding to Richardson.

“Behind my back, Natasha had been taking singing lessons to sing it to me,” Neeson explained. “After the ceremony, we were all going in to start the night’s festivities, and she grabbed the microphone, and she sang me this. I was like, ‘Wow.’”

Richardson’s song of choice? Van Morrison’s 1970 hit “Crazy Love.”