The pair, both among the cast of the upcoming The Private Lives Of Pippa Lee, are allegedly getting close on the film's set.
An insider said: "They spend a lot of time in each other’s trailers and they are also always hugging on the set. The chemistry is really electric."
Reeves and Ryder also starred in Francis Ford Coppola's 1992 film Dracula.
Reeves was previously rumoured to be dating actress Parker Posey.
The Matrix actor hasn't been in a long-term relationship since girlfriend Jennifer Syme died in a car accident in 2001.