Olsen, who split with businessman David Schulte recently, was spotted with Miller at the funeral of Philip Seymour Hoffman last week.
Miller was a close friend of the late actor. He directed 2005's movie "Capote" which helped Hoffman win a Best Actor trophy, reported Us magazine.
"They were introduced and have started dating," a source claimed.
The 27-year-old fashion designer reportedly spent her time with Miller in Los Angeles in January while he was editing his new project "Foxcatcher".
The two were seen eating together on January 24 at Dan Tana's in West Hollywood.
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