The actress, 51, was seen being flirty on the beach with musician Sean Friday, 27, while on vacation in Tulum, Mexico with her daughter Rumer Willis and friends.
"They've been hanging out together for months and by all appearances, it seems like they're dating," says a source.
Moore, who got divorced in November, certainly wasn't shy about packing on the PDA with her man during her Mexican getaway as they rang in the New Year.
Here are five things to know about Moore's new beau.
1. He's a drummer in the band Dead Sara.
Friday plays drums for the Los Angeles-based hard-rock band, which he joined in 2009. The group – which has toured with Muse – is best known for their song "Weatherman," off their 2012 album Dead Sara. Their next album is expected to be released by Epic Records this summer. Friday previously collaborated with Sonny Moore, better known as Skrillex.
2. Moore and Friday have been hanging out since early summer.
Moore was spotted backstage at a Dead Sara concert in Los Angeles, which she attended with her daughter Rumer Willis. The pair were seen together again leaving The Sayers Club in Hollywood on June 20, and were also spotted chatting at The Lot Party L.A. on July 14, where both Dead Sara and Rumer Willis performed.
3. He has several tattoos.
Friday's ink includes a large chest tattoo of an astronaut bearing wings, which is the Dead Sara logo. He also has an image of '60s supermodel Twiggy with her hands covering her mouth on his left bicep and a colorful treble clef on his right side.
4. He loves posting Vine videos.
While Moore has yet to make an appearance on his video-sharing account, Friday posts six-second videos regularly of himself singing and rapping (and, most recently, of the guy sitting next to him on a plane sleeping).
5. He's a wholesome guy.
"He is awesome," a source close to Friday tells PEOPLE, adding that he is not a big partier. "He is that guy you want to be with, just a fun guy."
With reporting by ELIZABETH LEONARD