According to US Weekly, the couple have been spending lots of time together in LA while Bennett makes the final cuts to his new film, and they were spotted on a dinner date at Dan Tana's in West Hollywood on 24 January.
They also supported each other at the funeral of Philip Seymour Hoffman in New York one week ago. Bennett, 47, was a close friend of the late actor, and also directed the 2005 film Capote, the biopic which earned Philip his only Oscar.
Ashley Olsen is said to be dating Bennett Miller
"They were introduced and have started dating," a source confirmed.
Following her twin sister Mary-Kate's trend of dating older men - she has been in a relationship with 44-year-old Olivier Sarkozy for almost two years - Ashley's new man is 20 years her senior.
Ashley was supported Bennett at Philip Seymour Hoffman's funeral
Ashley dated millionaire David, the CEO of luxury eyewear brand Oliver Peoples, for less than six months.
The former child star has always been low-key about her relationships; her last high-profile romance was with Hangover actor Justin Bartha, between 2008 and 2011. She has also been linked to designer Greg Chait and restauranteur Scott Sartiano.