The pair are both currently holidaying in The Hamptons and ran into each other at a James Taylor concert.
Paul, 64, and Christie, 53, are said to have slow-danced and "cuddled" during the romantic song "How Sweet It is To Be Loved By You," and spent most of the night together.
The former Beatle is currently going through a messy divorce with Heather Mills, while four-times married Christie is in the process of divorcing architect Peter Cook, who she wed in 1996 and split from in 2006.
However, Christie's second husband Billy Joel is doubtful the pair will become an item, and insists she knows the "Yesterday" singer through him.
Musician Joel told US TV show "Extra": "I know Paul from a long time ago, many, many years ago. We knew Paul, his late wife Linda and their children."
"I think Christie knows him from the same way, they're just old friends."
Paul agreed to go on vacation to the fashionable US resort at the same time as his estranged wife Heather, 39, so the custody arrangements of their three-year-old daughter, Beatrice, wouldn't be disrupted.
The pair's attempts to put on a "united front" for the sake of their daughter have seemingly failed.
This week, the legendary musician sailed alone in his boat, named "Linda" after his first wife, while Heather played pool in a nearby bar with a male friend.
