"How lucky am I to celebrate my birthday with these two??? I love you girls. So much," Cox captioned Saturday's photo of the three women smiling together.
Aniston is 50 and Kudrow is 55.
Aniston said in a TV interview on June 5 that she is up for a televised reunion with her former cast-mates should a revival or sequel ever get the green light.
"Anything is a possibility," she told the host of The Ellen DeGeneres Show. "Listen, I told you this. I would do it! The girls would do it, and the boys would do it, I'm sure."