Masatoshi Okauchi/Rex Features
The Matrix actor was spotted sharing a seat with Posey at Los Angeles's Chateau Marmont Hotel last week.
A source said: "They were sharing a seat and sitting very, very close. They were laughing and joking, and looked as though they were having a really good time. But it was probably the oddest couple I've ever seen!"
Posey and Reeves first met in 2004, when she approached him about a role in a silent action-adventure movie.
Reeves's last long-term relationship ended in 2001, when girlfriend Jennifer Syme died in a car crash.
Dazed and Confused star Posey has previously been romantically linked to musician Ryan Adams and writer Thomas Beller.
