The Manhattan billionaire President Obama wanted to appoint ambassador to France turned down the prestigious position over ties to an alleged Russian mob-run poker ring that was laundered through a Carlyle hotel art gallery, sources told The Post.

Marc Lasry, who runs the $12 billion investment firm Avenue Capital in Midtown, withdrew on Tuesday because of his close friendship with Illya Trincher, 27, who was busted last week with 30 others, including Trincher’s pro-poker-playing father, Vadim, and brother Eugene.

The feds last week accused Illya Trincher of running the New York arm of the $100 million betting and money-laundering racket with world-renowned Manhattan art dealer Hillel “Helly” Nahmad.

“Marc Lasry is a big-time gambler, in golf and poker,” a source told The Post. “He’s a ‘master of the universe’ type, and he was friends with the kid Trincher.”

Lasry, 53, turned down the post only days after the White House asked the FBI to probe whether he was tied to anyone involved in the criminal enterprise, sources said.

His name surfaced in FBI tapes probing the matter as a person who likes to play in exclusive high-stakes poker games, sources said.

Because ambassadorships require Senate approval — normally a pro-forma step — Lasry faced the prospect of being grilled about the ring.

“It’s not that he committed a crime, but it opens a can of worms,” a source said.

In mid-March, Bill Clinton, a close friend of Lasry, said at a fund-raiser that Lasry was Obama’s pick for the ambassadorship. Once a big Clinton donor, Lasry was one of the few Wall Street honchos to stick by the Democrats in 2012, raising nearly $1 million for Obama’s re-election campaign.

The hedge-fund king and other high-rollers can wager up to $2 million in the poker games, which were held in apartments worth $20 million or more, sources said.

The ring took bets “from celebrities, professional poker players and very wealthy individuals working in the financial industry,” the criminal complaint says.

Among the defendants is a Russian national, still at large, who also is accused of trying to fix the 2002 Winter Olympics skating competition.

Others arrested included “Poker Princess” Molly Bloom, who has organized poker games for celebs including Leonardo DiCaprio and Tobey Maguire.

Nahmad, himself a high-stakes gambler, allegedly helped launder “tens of millions of dollars” from the bookmaking ring through his Carlyle hotel gallery.

Nahmad controlled his family’s $3 billion art collection.

Lasry has been known to play in informal games with other wealthy investors, including Boaz Weinstein, founder of hedge fund Saba Capital Management, and David Bonderman, head of private-equity giant TPG Capital.

“I have a rule. Never play cards with Marc for money,” Bonderman told the trade publication Institutional Investor in 2007.

The publication reported that Lasry often hosts winner-take-all card games in his Upper East Side mansion, where the stakes can get as high as $20,000 per hand.

Last year, Lasry spoke on Bloomberg TV of his love for poker.

“Poker is math, so I enjoy playing it because I think there’s a lot of math involved,” he said. “And it’s fun. It’s fun to play with others.”

The White House had no immediate comment on the Lasry gambling allegations.

Lasry said “no comment” when asked about the gambling yesterday as he rushed into his home on East 74th Street.

A spokesman for Avenue Capital said, “Marc withdrew because it was becoming difficult to receive a waiver of the ‘key man’ provision from Avenue Capital’s investors, and he would have had to divest himself of his Avenue Capital business holdings.”

Lasry told Avenue Capital investors on Tuesday that he was staying put at the hedge fund, which invests in distressed debt.

In a letter, the Moroccan-born financier cited “recent speculations regarding the possibility that I might be asked to serve as the next US ambassador to France.

“I am very grateful to have been considered, but I would like to put the speculation to rest and let you know that I will be remaining at Avenue,” he wrote.

Lasry’s withdrawal raised eyebrows because he was known to badly want the ambassadorship. Before he withdrew, Lasry was planning to move his family to France and turn over management of Avenue to others.

In March, Avenue appointed its first chief investment officer since Lasry founded the firm with his sister, Sonia Gardner, in 1995.

A source close to Clinton said, “Lasry loves playing cards. He played in a celebrity poker tournament for Clinton’s foundation.

“I can’t believe that Obama admits in a book that he snorted cocaine and yet Marc Lasry can’t be named ambassador to France because he played cards.”

Additional reporting by Geoff Earle, Bruce Golding and Lia Eustachewich