The couple, who have been dating for more than a year, were seen together in New York earlier this week. According to The Mirror, Radcliffe met Coker when she worked on the set of the final three Harry Potter movies.
Coker, 22, is also believed to have been part of the crew on Radcliffe's next cinema release The Woman In Black.
The 22-year-old actor previously confirmed that he was in a relationship, telling chatshow host David Letterman that he is "very much in love".
Coker's painter and decorator father Malcolm told The Sun: "They have been going out for just over a year now. I'm just really happy for Rosanne and as long as she's happy that is all that matters to me.
"Who knows where it is going to lead? She still lives over here in London and he is in New York a lot. But they have a lot of fun together and at their age what more could you ask?"
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Watch the trailer for Radcliffe's new film The Woman In Black below: