When asked by the Stallones if he ever got nervous introducing his previous girlfriends to Schwarzenegger, 74, Baena said, "No, it was fine."
"I also have to point out that with my relationship with my dad it took a little while for me and him to get really close and just [feel] like I can joke around with him and talk about anything," he continued.
Baena was born in October 1997 to Schwarzenegger and the actor's former housekeeper Mildred Patricia Baena.
"I grew up with my mom and I was always nervous and I didn't want him to think bad of me and be like, 'What the heck is this guy doing? He's just partying all the time,'" Baena said. "Now it's like awesome. I'm so close to my dad and we joke about everything."
Joseph Baena/instagram Arnold Schwarzenegger and Joseph Baena
Baena also revealed a cheeky side to the former California governor, saying Schwarzenegger "always wants to hear about the drama. He's like, 'Tell me everything, tell me about the drama, tell me about the girls.'"
Baena, who has embarked on his acting career in the last couple of years, also revealed why he hadn't taken on his famous father's last name.
"I never had the Schwarzenegger name. I think really the thing is that I haven't focused on changing it," he explained. "I'm doing my own thing. I haven't thought of it that much. I have a last name already. I'm already doing so much and succeeding and moving forward with my goals. That's the last thing on my mind."
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While they may not share the same last name, Baena can periodically be seen sharing photos of himself and his Terminator dad on his Instagram account and vice versa.
In October, Schwarzenegger celebrated his son's birthday with a trio of photos of time spent together.
"Happy birthday Joseph! I am so proud of you and I love you! You are crushing it in the gym, in your real estate career, and in acting," the proud dad wrote alongside the post. "I know this will be another fantastic year."