"We're friends," Marie tells PEOPLE. "He's a great guy. He's funny and sweet."
Sources say Marie, 23, and Mayer, 31, met in 2008 at the Beverly Hills cigar club Grand Havana Room, where she currently works as a bartender and cocktail waitress.
Although the pair have not stepped out publicly, "they've spent time together over the past few months," a source tells PEOPLE. "They're enjoying getting to know each other."
Marie is also an aspiring actress – she guest stars as Maria, the pizza delivery girl of the Jonas Brothers' dreams on their upcoming TV show JONAS, which debuts on the Disney Channel on May 2. (Marie's episode airs May 16).
The former model, who has appeared in ads for Pioneer, Doritos, Nissan and Toyota, graduated in 2006 with a bachelor's degree in broadcast journalism from Azusa Pacific University.
Meanwhile, Mayer has been holed up in his home studio in L.A.'s San Fernando Valley working on his next album, tentatively titled Battle Studies.
Eric McCandless / Disney Channel