The 21-year-old, who played Buffy's sister Dawn Summers in the show, has been seen out with Williams, 32, for a few weeks now.
A source close to the pair said: "Robbie really likes Michelle — he especially loves her sense of humour. They're having a great time just hanging out."
The source source continued: "As we all know, Robbie doesn't have a high celebrity profile in the States despite many attempts to launch his career over there.
"So as far as Michelle is concerned, she's just spending time with a normal bloke from a place called Stoke. That's just how Rob likes it."
The pair were also snapped while shopping at Fred Segal.