Matt Rutler "gave [a ring] to her for her birthday," a source tells PEOPLE. "It's not an engagement ring and they're not engaged. It was a surprise gift from him."
Although the lovebirds aren't necessarily saying "I do" anytime soon, they are getting more serious. Rutler's mom has had the honor of meeting Aguilera. And Rutler was by Aguilera's side at her New Year's Eve bash, which was attended by her own mother, brother and sister.
Aguilera recently introduced Rutler to her son Max when she brought him to the Peterson Automotive Museum in L.A.
"Christina took Max on the fun outing so he could bond with Matt," a source says. "Max was initially a bit shy, but later warmed up to Matt. It seems very important to Christina that Max got along with Matt."
The source also says Rutler has been spending the majority of his time staying at Aguilera's Beverly Hills home, while the singer's ex, Jordan Bratman, is now living in a rental home nearby.
With additional reporting by PERNILLA CEDENHEIM