The French singer, who split from Depp after 14 years together in June, is reportedly uncomfortable with the idea that Heard could become close to the former couple's children, Lily-Rose, 13, and 10-year-old Jack.
"Vanessa's devastated that Johnny's dumped her," an insider told Now.
"She blames Amber and calls her a man-stealing, two-bit nobody and has vowed to not let her anywhere near their children."
The publication also claims that Paradis and Depp are set to meet for a showdown over the details of the split.
Depp and Heard have been romantically linked since news of his split from Paradis broke. Rumours intensified once it was revealed that the bisexual actress had broken up with her girlfriend earlier in the year.