32-year-old Kerr, who has son Flynn, four, with ex-husband Orlando Bloom, is thrilled her mother, Therese, and father John gave the Snapchat founder their seal of approval during a trip to Greece in July, reported Female First.
"She thinks he's sweet. It's gotten serious fast," a source said.
The billionaire, 25, has also developed a close bond with Flynn. "Miranda is super into him. It's hot and heavy," the insider said.
The couple, who started dating in June, were spotted boarding a flight at Los Angeles International Airport earlier this week and are planning to enjoy their first romantic holiday together to Paris.