Credit: Jeff Vespa/VF12/

Jennifer Lopez has fallen hard for backup dancer Casper Smart, but not enough to marry him -- yet.

The American Idol judge's rep denies a Star magazine cover claiming the two secretly tied the knot in Mexico and that Smart, 24, wants to adopt her 4-year-old twins Max and Emme (with ex-husband Marc Anthony, 43).

"This story is completely false," Lopez's rep tells Us Weekly of the tabloid report.

Lopez, 42, is simply happy to be in a less complicated relationship with Smart after splitting with Anthony, her husband of seven years, last July.

When Today co-host Matt Lauer grilled Lopez in January about whether she'll ever marry again, the flustered singer responded: "I don't know. I don't know. I don't know. We'll see. I mean, I don't know. It's not time to think about that yet. It's still fresh."

In the April issue of Vogue, Lopez's manager (and her twins' godfather) Benny Medina gave insight into why she's so smitten with Smart, who recently directed her "Follow the Leader" music video in Acapulco, Mexico.

"She's not oblivious to her own reality right now, as in, 'Damn, I'm 42 with a 24-year-old. Why?'" Medina said. "We talked about it yesterday. She was just like, 'It's not even the age, Benny. It's that I just came out of a relationship where I felt like I was kind of not getting what I needed. And I'm open! So somebody who steps in right now and is actually touching me in a way.' It's very fertile ground."