Miller, who met her former finance Jude Law on the set of "Alfie," was in Canada meeting the family of Christensen, her co-star in "Factory Girl," the Daily Mail reported Friday.
The pair have been seen shopping and smooching together since meeting on the set of "Factory Girl," in which Miller plays the doomed Edie Sedgwick and Christensen portrays singer/songwriter Danny Quinn, the newspaper said.
"Sienna is quite flirty and their friendship became something more," a source close to Miller told the newspaper. "Hayden is besotted with Sienna but I'm not so sure that she totally reciprocates his feelings."
Notable deaths of 2014 [PHOTOS]