The Transformers star reveals he became "infatuated" with the "Umbrella" hitmaker and was stunned to find out Rihanna was trying to get in touch with him.
A mutual stylist friend eventually passed Rihanna's details to LaBeouf while he was filming Indiana Jones and the Kingdom of the Crystall Skull in Hawaii.
He recalls, "(I was) filming a sword fight when I got the message. I said to myself, 'Can this be my life?'"
The actor tells Playboy magazine he texted the R&B pin-up and they set up a dinner date: "It never got beyond one date. The spark wasn't there. We weren't passionate about each other in that way, so we remain friends."
LaBeouf admits the passion definitely was there on the Transformers movie sets -- between him and co-star Megan Fox, who plays his girlfriend in the action blockbusters.
And the actor still holds out hope he and Fox can become lovers in the future.
He admits they both had to be professional about their relationship while they were working together: "It hasn't been a romantic thing because you're trying to respect the work environment. You don't push anything. And, with sex and romance, things become convoluted so fast... You're playing with the devil.
"We could be shooting, and the relationship is suddenly on the rocks and then what? So we just never did anything about it. We were very smart. We're attracted to each other, and I think you can see that in our scenes together. It's very real and tangible, and you can tell something exists.
"I'm going to know the girl forever. She's a beautiful, intelligent girl, and when you make a movie with someone like that... you feel things. I know a relationship between us isn't an option for us right now for a variety of reasons... (but) I get to kiss her in the fantasy world."
Fox is involved in a committed relationship with actor Brian Austin Green, but the couple recently called off its engagement.
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