Pattinson, 27, first sparked dating rumours after he was spotted catching a show with Dylan, 22, at the famed Viper Room in LA earlier this month, reported People.
"They've been dating a month or two. He's crazy about her," a source told the magazine.
Pattinson's love life has been under the media scrutiny following his break-up with Kristen Stewart about four months ago.
Pattinson and Stewart found love while filming the vampire romance series but suffered a setback when Stewart's affair with her 'Snow White and the Huntsman' director Rupert Sanders became public.
Pattinson has been linked to many women post-split including his trainer Sydney Liebes but a source denied that there was any romance.