McCartney dance sparks romance rumours
The pair – who are both in the process of divorcing their partners - bumped into each other at a James Taylor concert while vacationing in the Hamptons.
The Beatles legend is in the US resort at the same time as estranged wife Heather Mills in an effort to ensure that their daughter Beatrice's custody arrangements are not interrupted.
Paul, 64, reportedly spent most of the evening laughing and joking with 53-year-old Christie, and the couple "cuddled" while dancing to the song 'How Sweet It is To Be Loved By You'.
But Brinkley's second husband Billy Joel has dismissed the rumours, saying the pair are just "old friends".
He 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."