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"There's a few different variables in that," Joseph, 24, said on E!'s Daily Pop. "But that's just not my main priority at the moment, so I'm just focused on building myself up and building my career in acting and real estate and just focusing on that right now."
That said, Joseph — who has been filming the Bitflix action thriller Lava — and his famous dad, 74, are close.
"I mean, my dad is a stallion," Joseph said. "He's a man's man, I like to think, and I look up to him a lot. So in a way, he's influenced a lot of things: the path that I have taken with acting, with fitness and my physique and the many other things that I'm doing."
He also said he's looking forward to spending "the holidays is my family," but didn't specify exactly who that included.
Joseph's family history is of course complicated. In 2011, it was revealed publicly that Arnold, who was married to Maria Shriver, had fathered a child with their long-time housekeeper Mildred Baena. Shriver filed for divorce that year. (Ten years later, the divorce is still pending.)
Mildred and her then-husband Rogelio Baena, who was apparently unaware of the child's true paternity, raised Joseph. Arnold has said that when Joseph was 7 or 8 it became apparent that he was the father because the child looked so much like him.
It's unclear if Joseph ever legally changed his last name to Schwarzenegger. It was Baena on his birth certificate.
While Joseph is close with Arnold, his relationship with his Schwarzenegger half-siblings — Patrick, Katherine, Christina and Christopher — is murkier. They don't pop up on one another's social media pages, despite lots of Schwarzenegger sibling shout-outs. However, Jospeh was once seen working out with Patrick, who is also an actor.
On the other side of the family, Arnold has gotten to spend at least some time with Joseph's half-brother Roger Baena. Arnold, Joseph and Roger celebrated Joseph's 24th birthday together at Arnold's home in October.
Joseph graduated from Pepperdine University in 2019 and started a residential real estate career which he now juggles along with acting. In addition to the film Lava, which sees Joseph going shirtless during a vacation gone wrong with a bunch of 20-somethings, he has a role in the film Chariot, which John Malkovich stars in and is expected in 2022.