TIGER WOODS wanted to get back together with his ex-wife Elin Nordegren and have more children – but when she nixed that plan, the horndog golfer pub­licly admitted that he’s dating Olympic skiing champ Lindsey Vonn.

And he’s already gushing about what great babies they’ll make!

A source confided to The ENQUIRER: “Tiger told Lind­sey, ‘I want to have children with you – twins if we get lucky. Imagine what world-class ath­letes they’d be!’ And Lindsey’s all for it, even if it means hang­ing up her skis for a while.”

That’s the big secret behind Tiger’s surprise announcement about his romance with the sexy alpine skier after spend­ing months trying to iron out a pricey prenup deal with Elin.

“Tiger felt that if he reunited with Elin, he could get back on top – both personally and pro­fessionally,” a source revealed.

“BUT he wants more children, and Elin doesn’t – it’s that simple. When their reunion discussions broke down, Tiger de­cided to let the world know that he’s dating Lindsey.”

Lindsey, a 28-year-old Elin look-alike, post­ed photos of herself and Tiger on her Facebook page and wrote: “Our relationship evolved from a friendship into something more over these past few months, and it has made me very happy.”

Tiger followed by posting the same photos on his Facebook page, and wrote: “Over the last few months, we have become very close and are now dating.”

The links legend’s five-year marriage to Elin, 33, im­ploded in 2009 when The ENQUIRER revealed that he was having an affair with New York party girl Rachel Uchitel. After that, a parade of bimbos told of their affairs with Tiger.

The cheating golfer, 37, shelled out a report­ed $110 million to divorce Elin, and kissed off millions more in lost endorsement deals while his golf game collapsed.

But as The ENQUIRER reported, Tiger offered to sign a $250 million no-cheat prenup if Elin would remarry him. She countered by demanding $350 million, which is more than half of Tiger’s fortune.

The couple – who have daughter Sam, 5, and son Charlie, 4, together – lived in a trial marriage while negotiating the deal, and sources say Tiger desper­ately wanted to add to their family. But Elin, who’s been dating 55-year-old billionaire coal magnate Chris Cline, ultimately decided against rekindling her romance with Tiger, said the source.

“Elin felt she could never trust Tiger again,” said the source. “Besides that, she considers him juvenile and doesn’t like the public hoopla that surrounds him.

“She says Chris is more mature than Tiger, and she loves that he prefers to live his life out of the spotlight.”

During his prenup negotiations with Elin, Tiger dated Lindsey on the down-low. She’s had plenty of time for romance. In February, she broke a leg and tore ligaments after a high-speed fall put her out of action for the rest of the year.

“When Tiger’s golf game was in a slump, he was afraid Lindsey’s success would outshine him,” said the source. “But he’s won two tournaments this year, and feels that they’re on more equal footing.

“Now that they’re out as a couple, friends are wondering if an engagement announcement is on the horizon!”