No, not that president — the Austrian-born former governor of California isn’t eligible to become America’s commander-in-chief. But in a recent profile of the Governator in Newsweek, his former cabinet secretary put forward his name as a possible president of the European Union.

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 the 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?”

As governor, the Republican Mr. Schwarzenegger showed an independent streak that sometimes irked his allies and enemies alike. Whether Europe’s leaders would see that independent-mindedness as a virtue is unclear. The current president of the union is Herman van Rompuy, a retiring and technocratic former Belgian prime minister who mostly stays in the shadows and works behind the scenes. A Schwarzenegger presidency would be a different beast altogether, and it would certainly give the Brussels-based European Union star power on the international stage.

Since he left office, Mr. Schwarzenegger has announced a return to acting. And for some Europeans, his long attachment to America — it’s been decades since he left Austria to make it as a movie star stateside — could prove disqualifying. Still, he’s already shown a taste for politics. Watch out, Europe — it’s just possible that Mr. Schwarzenegger could be back.