He asked the question at the annual festival that celebrates the performing arts.
The 54-year-old "Pirates of the Caribbean" star followed by saying that he is not an actor, but someone who lies for a living.
However, he said, it's "been a while, and maybe it's time."
In a statement to ABC News, the Secret Service said: "We actively monitor open source reporting, including social media networks, and we evaluate potential threats. For security reasons, we cannot discuss specifically nor in general terms the means and methods of how we perform our protective responsibilities."
ABC News has asked both Depp's publicist and the White House for comment.
It's possible that Depp may have been referencing actor John Wilkes Booth, who assassinated President Abraham Lincoln in 1865.
Depp was at the festival to introduce a screening of his 2004 film "The Libertine."
He played Trump last year in a Funny or Die video parody of the businessman's 1987 book "The Art of the Deal."
Last month, comedian Kathy Griffin's infamous beheaded Trump video pit the president's supporters against Hollywood.
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