The 41-year-old two-time Emmy winner responded Wednesday on Twitter after "The West Wing" creator Aaron Sorkin suggested Brown for a potential revival.
"#AaronSorkin if you are serious, sir, I would be honored," he wrote, adding an American flag emoji.
Sorkin had divulged in a new interview with The Hollywood Reporter that he occasionally considers NBC's standing offer to reboot "The West Wing."
He said original star Martin Sheen, who played President Jed Bartlet, would also have a role.
"Sterling K. Brown as the president, and there's some kind of jam, an emergency, a very delicate situation involving the threat of war or something, and Bartlet, long since retired, is consulted in the way that Bill Clinton used to consult with [Richard] Nixon," the producer suggested.
Sorkin said he has a harder time envisioning how Allison Janney and Bradley Whitford's characters, C.J. Cregg and Josh Lyman, would fit in the new scenario.
Richard Schiff, who played Toby Ziegler, said in August that he had spoken to Sorkin about a reboot.
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"I did have a particular idea that I spoke with Aaron about," the actor said on "PoliticKing with Larry King," according to the New York Daily News.
"And I love my idea. I don't know if that's going to happen."
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