It's a script drawing laughs and frowns among European Union veterans: Arnold Schwarzenegger, EU president, chairing summits next to Nicolas Sarkozy, Angela Merkel and David Cameron.
News that the Austrian-born former "Governator" of California was advised to seek the EU presidency has brought smiles to the staid corridors of Brussels, but also exasperation about the EU's image in the United States.
"It gave me a pretty good laugh," Guy Verhofstadt, former Belgian prime minister and head of the European Parliament's Liberal group, told AFP.
Turning serious, he sighed that it "shows a total lack of knowledge of Europe," noting it must be confusing for Americans to know who's at the helm when the EU has a European Council president and a European Commission president, each of whom tries to rival the top national figures.
Joerg Leichtfried, a fellow Austrian Social Democrat member of the European Parliament, was less amused, saying talk of Schwarzenegger bidding for the European Union presidency feels "scurrilous."
"April Fool's Day has come and gone," he said.
Joke or not, Schwarzenegger would have his first shot at the post in mid-2012, at the end of the first two-and-a-half-year term of European Council President Herman Van Rompuy, a button-down former Belgian premier.
But "Conan the Barbarian" can forget about flexing his political muscle against the haiku-writing Van Rompuy in a US-style presidential campaign.
Instead, the action hero would have to charm and cajole 27 people with their own big egos: the bloc's 27 heads of state and government, the only people who get to nominate and vote for the EU Council president.
Schwarzenegger has been looking for work since his two terms as California governor ended in January, but is barred by the US Constitution from running for president because he was born abroad.
His former cabinet secretary says he told Schwarzenegger he should stand for EU president.
"In the next few years, the EU will be looking for a much more high-profile president -- somebody who can unify Europe," Terry Tamminen told Newsweek magazine.
"The French won't want a German, and the Germans won't want an Italian. How about a European-born person who went off to America and -- could return to be the Washington or Jefferson of a new unified Europe?" he said, referring to America's founding fathers George Washington and Thomas Jefferson.
But would a Hollywood star used to the limelight say "Hasta la vista, baby" to sunny California to audition for a role in dreary Brussels in the first place?
The EU Council president, a job created in December 2009, is little known outside Brussels and has limited powers, chairing EU summits and mediating the wants and needs of 27 often-bickering capitals.
The first question, however, is whether Europe wants the "Terminator."
EU leaders are unlikely to choose someone who will take the spotlight away from them, observers say, pointing out that the low-key Van Rompuy was picked over outspoken former British prime minister Tony Blair in December 2009.
"Someone with an American style of politics with outspoken ideas would absolutely not be appreciated by EU leaders. They want an absolutely grey person," said Peter Cleppe, head of the Open Europe think tank in Brussels.
It could be a different story if the EU president was elected by the people. A bill under debate in the EU Parliament could ultimately allow voters in the future to choose the head of the bloc.
"If there was a pan-European election I wouldn't immediately say that his chances would be so small. Schwarzenegger is a person who is known at least all over Europe. He can say he was governor of California," Cleppe said.
Staunch eurosceptic Nigel Farage, a British member of the European Parliament, gives his own inimitable take.
"I like Arnie, he's a character," Farage told AFP. "As the Terminator, I hope he will put an end to the EU."
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