“[Justin] is set on proving that he is a better boyfriend,” the source added.
However, with Christmas fast approaching, the pair will be going their separate ways to spend the holiday with their respective families.
“Justin’s family always loved Selena, but Selena’s family is still not happy about her seeing Justin,” the source explains. “Selena doesn’t bring Justin to any family events. Selena is spending Christmas with her family. As of now, Justin is not invited.”
“They just backed off a little from being out there and are being a bit more low-key,” an insider shared with PEOPLE in November, adding that Bieber, 23, and Gomez, 25, are still not officially boyfriend/girlfriend yet “but it’s getting close.”
WATCH: Justin Bieber & Selena Gomez Are ‘Figuring Things Out’ But Not Boyfriend/Girlfriend Yet
In fact, Gomez has never been able to get over her first love.
“Justin was Selena’s first love. He will always have a special place in her heart,” a separate source said. “She’s always held out hope that one day the circumstances and timing would be right.”
Also last month, Gomez briefly explained her reunion with Bieber to Billboard. “I’m 25. I’m not 18, or 19, or 20,” she said. “I cherish people who have really impacted my life. So maybe before, it could have been forcing something that wasn’t right. But that doesn’t mean caring for someone ever goes away.”
And on Saturday, Bieber’s mother, Pattie Mallette, raved about Gomez to PEOPLE, saying, “I don’t know so much about their personal relationship because [Justin] doesn’t share a whole lot, but I love her. I support anything [he does], if he loves her I love her, and I’ve met her and we have a special bond so I think she’s precious.”