The 62-year-old model has been married four times - to François Allaux, Billy Joel, Richard Taubman and Peter Cook - and is now reportedly charming the 67-year-old musician as the pair were recently spotted on date at Ralph Lauren's Polo Bar in New York City, where former US Secretary of State Hillary Clinton was also dining.
A source told New York Post's Page Six column: ''Christie and David were on a date, and Hillary came over and greeted them. She gave Christie a warm hug.''
The pair were then seen heading to a show by horn player Chris Botti at the Blue Note Jazz Club, with another source describing them as ''looking cozy''.
For David - who has also been married four times to BJ Cook, Rebecca Dyer, Linda Thompson and Yolanda Hadid - the reported romance comes a year after he split from his most-recent wife Yolanda, who is the mother of models Gigi and Bella Hadid.
The pair split in December 2015, and the 52-year-old 'Real Housewives of Beverly Hills' star filed for divorce in January after her Lyme disease diagnoses put a strain on their relationship.
Yolanda said at the time: ''We had a beautiful love story that I will treasure forever. Unfortunately, it was not strong enough to withstand the circumstances that came our way.
''Chronic, long-term illness is extremely challenging. Not only for the person sick but also for the caregiver. It for sure changed the dynamic of the relationship.
''The truth is that we both worked through the difficult time through the best of our ability, so rather than judging what went wrong, I pick to remember the great times that we shared the last nine years. There was a wealth of good times.''