The 56-year-old actor and 50-year-old actress both attended the awards show Sunday at the Beverly Hilton Hotel in Beverly Hills, Calif.
Pitt and Aniston were married from 2000 to 2005. Pitt went on to wed actress Angelina Jolie, from whom he split in 2016 after two years of marriage and more than 10 years together.
Pitt said in an interview with Entertainment Tonight on the Golden Globes red carpet that he was open to a run-in with Aniston.
"I'll run into Jen! She's a good friend," Pitt said.
"The second most important reunion of her year," he jokingly added, referencing Aniston's reported Friends reunion special at HBO Max.
Sources told E! News Aniston was seen clapping, laughing and standing up for Pitt during the actor's acceptance speech for Best Supporting Actor in a Motion Picture for his role in Once Upon a Time in Hollywood. Pitt joked about attention to his personal life in the speech.
"I wanted to bring my mom, but I couldn't. 'Cause any woman I stand next to they say I'm dating," he said. "It would just be awkward."
Pitt and Aniston both attended the CAA after-party following the Golden Globes. E! News said the pair had a brief interaction during the bash.
"They said hello very quickly," a source said. "It was brief, but [they] were very cordial and friendly and seemed happy to be there."
In addition to Pitt's win, Once Upon a Time in Hollywood also took home Best Motion Picture -- Musical or Comedy, while Tarantino won Best Screenplay.