TIGER WOODS is risking his romance with LINDSEY VONN by chasing after busty “Sports Illustrated” cover girl KATE UPTON!

Tiger, 38, and Olympic skiing champ Lindsey, 29, have been dating for more than a year. As The ENQUIRER re­ported, she’s recently been pressing him to pop the question – even using a com­ment Michael Douglas made about her to make Tiger jealous. But now, insiders say the only question Tiger’s interested in asking is how he can hook up with 21-year-old blonde bombshell Kate!

“Tiger has been drooling over Kate like a giddy teenager and has told friends she’s the most beautiful wom­an he’s ever laid eyes on,” confided one insider. “He spends hours staring at her photos online and has been trying to score invites to cocktail parties in New York so he can bump into her.

“He’s even been asking around for her number and has made the slimy prediction that it’s only a matter of time before they wind up together.”

Michigan-born Kate – who recently turned to acting and landed a role in “The Other Woman” along­side Cameron Diaz – burst onto the fashion scene in 2011 when she was named “Rookie of the Year” for her stunning swimsuit poses in “SI.”

Since then, her killer curves have earned her a legion of male fans around the globe. A 2012 YouTube video – which featured the buxom beauty doing a steamy dance called “Cat Daddy” while wearing a bikini – went viral and solidified her status as a sex symbol.

Serial womanizer Tiger was married to Swedish beauty Elin Nordegren for six years. But their marriage exploded in 2009 after The ENQUIRER re­vealed he’d cheated on her with New York party girl Rachel Uchi­tel, and several other women emerged to claim they’d also had affairs with him. And Kate – who was recently linked to Detroit Tigers pitcher Justin Verlander – is exactly the kind of woman he finds irresistible.

“Tiger says Kate’s got a body to die for and a smile that’s nothing short of magical,” the insider added. “He loves Lindsey, but this crush he has on Kate won’t go away, and he’s determined to see it through, whatever the conse­quences.”