Katharine McPhee and David Foster Perform Together at Star-Studded Holiday Party

Katharine McPhee and David Foster are getting into the Christmas spirit!

On Saturday, McPhee, 33, and Foster, 68 — who were spotted locking lips in November but have yet to officially confirm their romance — shared the stage at Academy Award-winning singer-songwriter Carole Bayer Sager and her husband Bob Daly’s holiday party.

Kim Kardashian — who documented the party on her Instagram story — shared a video of the musicians performing “White Christmas” alongside producer and singerKenneth “Babyface” Edmonds.

The Keeping Up With the Kardashians star also shared a video from McPhee and Foster’s rendition of “Grown Up Christmas List,” in which the 33-year-old singer appeared to be reading the lyrics off of her cell phone.

The party — which Kardashian described as “legendary” — also featured festive performances from Keith Urban, Hugh Jackman and Joe Walsh.

Rumors about Foster and McPhee’s relationship started in September after the Grammy-winning producer’s daughter Erin Foster shared photos of the pair at the Grammy Museum’s third annual gala at the Novo in Los Angeles, writing in the caption, “Excited about my new step mom.” (A source close to the situation told PEOPLE at the time that the social media posts were a joke.)

In October, the two were also photographed walking arm-in-arm in Brentwood, California, but a source told PEOPLE at the time that the pair were merely having “some fun” at the expense of photographers.

And most recently, the pair were spotted in Beverly Hills sharing a kiss on the lips.

Speaking about the relationship rumors, McPhee previously told PEOPLE that she had “zero desire” to address them. “It’s great that they want to do that. I think it’s so amusing that people are amused by my love life,” she added.

“Here’s how I look at it: I’m not doing anything wrong, so whether people think it’s true or false, I don’t, you know, there’s nothing bad happening in my life, so people can just say whatever they want,” she said.

McPhee and Foster have been friends for years, first meeting on the set of American Idol when McPhee was a contestant in 2006.

Although their romantic status remains uncertain, in October Erin had nothing but kind words to say about McPhee. “She’s amazing. I really like her. She’s awesome,” Erin, 35, told PEOPLE. “My dad is kind of a hopeless romantic, and Katharine’s awesome. We really, really like her, and we’ve known her for a really long time. And if he’s happy, we’re happy.”

And despite the fact that he’s been through four divorces — most recently finalizing his separation from Yolanda Hadid — the legendary producer is open to walking down the aisle again.

“It’s quite obvious by my track record that I love being married, so I wouldn’t say no to being married again,” Foster previously told PEOPLE. “I like the concept, I’m just not that good at it.”