Gary Oldman is open to starring in a Marvel movie, he said during an appearance at Sunday's Screen Actors Guild Awards.

“Marvel hasn’t called me,” Oldman told PEOPLE. “But now that you mentioned it, if they’re tuning in, my son wants me to!”

Oldman is father to Alfie, born in 1989, and teenagers Charlie John and Gulliver Flynn.

Oldman won the SAG trophy for outstanding performance by a male actor in a leading role for his performance in Darkest Hour, where he portrays Winston Churchill. The role won the actor a Golden Globe earlier this month.

He famously portrayed do-gooder Commissioner James Gordon in Christopher Nolan's Dark Knight trilogy, a role that has since been filled by J.K. Simmons in Warner Bros.' revamped DC Extended Universe.

Though he admits he's yet to see any of the newer DC Comics movies, Oldman had high praise for Simmons, calling him a "wonderful actor" in an interview with ComicBook.com.

"Gordon was very good to me so I wish him a lot of luck," Oldman said. "I'm excited for him."

Simmons made his debut as Batman's longtime and trusted ally in November's Justice League.

Oldman's appearance at the SAG Awards wasn't without controversy: his critically acclaimed role in Darkest Hour and subsequent media attention resulted in backlash aimed at the actor on social media.

Twitter users referenced Oldman's past domestic abuse accusations, citing a specific incident of alleged spousal abuse against ex-wife Donya Fiorentino.

Hit-factory Marvel Studios boasts the shared Marvel Cinematic Universe, which has since crossed $5 billion at the domestic box office — the first franchise to accomplish the feat.

Marvel is known for attracting pedigree to its blockbusters: their films have seen supporting roles filled by veteran actors Jeff Bridges, Tommy Lee Jones, Anthony Hopkins, Robert Redford, Glenn Close, Angela Bassett, and Forest Whittaker.

Marvel will next release Black Panther, in theaters February 16, followed by superhero epic Avengers: Infinity War May 4 and Ant-Man and the Wasp July 6.