The rumors have been swirling for a few days now: The Washington Capitals have been talking to Wayne Gretzky about becoming team president. Those rumors are probably just aimless speculation around a general manager job that has been vacant for nearly a month, but the idea is worth considering.

Almost as soon as the chatter began, people began scoffing at the thought: The Caps have a team president, Dick Patrick, and Gretzky’s career in both the front office and behind the bench in Phoenix didn’t work out. And perhaps most important, does anyone in town — most notably Ted Leonsis — remember the Michael Jordan fiasco?

Never mind all that. Give Patrick a nice title like vice chairman of the board and make way for Gretzky. We aren’t talking your run-of-the-mill ex-hockey player here. We’re talking Wayne Gretzky — the Great One. He is to hockey what Jordan was to basketball.

Which brings us to Jordan. Leonsis needs to ask Gretzky the one question he and Abe Pollin never put to Jordan: Are you willing to work at this job while living in Washington? If not, then move on. But if the answer is yes, sign him up.

Unlike Jordan, Gretzky would come to town with a legitimate post-playing-career résumé. He was general manager and then coach in Phoenix. Did he have success? No. But the Coyotes were a financial mess, eventually filing for bankruptcy, and that had nothing to do with any of Gretzky’s moves. In fact, in his first season as coach, the team improved markedly. He just never had the money or the support to build on that improvement.

Gretzky also has been involved in running Team Canada during three Olympics (as executive director in 2002 and 2006 and then as a special advisor in 2010) — not exactly a low-pressure job in a country that demands a hockey gold medal or bust in every Olympics. The Canadians won gold in 2002 and 2010 with a quarterfinal loss in between.

What’s more, Gretzky has the kind of personality that will make being an out-front guy for a franchise easy for him. Leonsis’s disdain for the media becomes increasingly evident every year, and during his rare public appearances, Patrick sounds as if he would rather be in a dentist’s chair than answer questions.

Gretzky was always approachable as a player, respected in the locker room not just because of his extraordinary ability but because he was “one of the guys” — a stark contrast to Jordan, who referred to teammates as “my supporting cast.”

The Capitals will be entering their 40th season in the fall. They have never won a Stanley Cup. They can go out and hire a standard-issue general manager and allow him to hire one of the very good coaches currently available. Come September everyone will talk about new beginnings and fresh approaches, and none of it will guarantee the team will be any better than the talented ones that fell short in the playoffs from 2008 to 2013.

But maybe instead Leonsis should think about what Gretzky — again, if he wants to work — can mean to a hockey franchise. Do you think there’s a bright young hockey executive or coach out there who wouldn’t want to work for Gretzky?

Maybe Gretzky would hire Mark Messier as coach. Do you think that would bring some fire to the locker room? Do you think Alex Ovechkin would ignore his back-checking responsibilities with Gretzky in the press box and Messier in the locker room?

There’s also the free agent issue. One of the sillier reasons George McPhee was fired as GM was the bleating of player agents who weren’t allowed in the locker room right after games. How many would voice such complaints to Gretzky’s face?