The 40-year-old actress has been spending time with Musk, 41, and the pair are said to be gelling very well, reports a website.
"Elon thinks Cameron is gorgeous. He personally sold her a Tesla earlier this year and they were flirting up a storm the whole time," said a source.
Cameron first met Musk after she bought an energy friendly sports car, a Tesla Model S EV, from his company earlier this year.
He has been travelling from Tesla's headquarters in Palo Alto to Los Angeles, California, on a regular basis to see her.