WASHINGTON (Reuters) - An unconventional debate between a billionaire Republican and a democratic socialist is shaping up in California after presidential candidates Donald Trump and Bernie Sanders expressed an interest in squaring off against each other.

Sanders, a U.S. senator from Vermont, is still in a primary battle against Democratic front-runner Hillary Clinton, while Trump effectively clinched the Republican Party’s nomination earlier this month when his two remaining rivals dropped out.

In an appearance on ABC’s “Jimmy Kimmel Live” late Wednesday, Trump said he was willing to participate in such an event against Sanders.

“If I debated him, we would have such high ratings,” the New York developer and reality television star said. “I think I should ... take that money and give it to some worthy charity.”

Sanders appeared to agree in a post on Twitter on Thursday.

“Game on,” he tweeted. “I look forward to debating Donald Trump in California before the June 7 primary.”

Trump and Sanders have gone through a series of debates against rivals within their parties but Republican and Democratic presidential candidates usually do not debate each other until the parties have selected a nominee.

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The hashtag #BernieTrumpDebate began trending in the United States with news of the possible debate.

Trump spokeswoman Hope Hicks said in an email to Reuters on Thursday there were no formal plans yet for such an event. Representatives for the Sanders campaign did not immediately respond to a request for comment.

Kimmel said he asked Trump about the debate at the suggestion of Sanders, who is scheduled to appear on the show Thursday night.

Sanders, a self-described democratic socialist who was elected to Congress as an independent and has made economic equality a keystone of his campaign, had first challenged Clinton to a California debate. He said he was disappointed when the former secretary of state declined. The Clinton campaign did not immediately respond to a request for comment to a possible Trump-Sanders debate.

Clinton has tried to woo Sanders supporters as she works to secure the party’s nomination for the Nov. 8 election. But some worry his supporters - who are largely young, working-class and disillusioned with party establishment - will turn instead to political neophyte Trump, who has championed a populist agenda.

Sanders has said he will do everything he can to ensure that Trump does not win the White House.