The 'Titanic' star and the 19-year-old beauty are rumoured to have fallen in love since meeting over New Year.
A source is quoted in Britain's News Of The World newspaper as saying: "Leonardo is besotted with Lindsay. They are a perfect match.
"They wanted to keep it a secret just because it's more fun that way."
The pair hooked up at a New Year's Eve party hosted by Lindsay in Miami. They have being seeing each other ever since - despite the 12 year age gap - and friends say they are helping each other get over their recent break-ups.
Lindsay had her heart broken by long-term boyfriend Wilmer Valderrama when he dumped her in December 2004, while 31-year-old Leo recently split with supermodel Gisele Bundchen after fiver years.
A friend of the pair said: "They had both come out of recent relationships so it was the perfect timing for both of them. Friends wouldn't be surprised if they settle down."