The actress had a fateful meeting with Gyllenhaal in a street more than 10 years ago, and was stunned to bump into him just weeks later while auditioning for the 2002 movie Moonlight Mile.
She explains, "I was... in the waiting room and the director and this guy, Jake Gyllenhaal, who I had never heard of - no one had ever heard of him at that point - walked past me. I (had) my head down... so I didn't get a look at Jake.
"I had met Jake a couple of weeks prior on the sidewalk! I walked into the (audition) room and I saw Jake and I said, 'Oh my God, it's you!' We sort of bumped into each other. He told me I was the most beautiful thing he had ever seen."
Director Brad Silberling noticed the palpable tension between the two during their tryout and asked if they were already acquainted.
Pompeo recalls, "We were like, 'No, we don't know each other. We made love to each other not speaking on the sidewalk, but we don't know each other!'"
But Pompeo admits she ruled out a romance with the hunky actor - because he's 11 years her junior: "I said, 'He's 12! And maybe we'll see each other again and I should leave!' There were sparks, but we just bolted... Listen, he is a handsome guy and a great actor (but) he is 20 years younger than me!"
Pompeo is now married to music producer Chris Ivery.