Lawson, 53, recently divorced the British art collector after he was photographed choking her at a London restaurant.
Saatchi has been sending Lawson harassing messages, begging her to contact him in the days after the couple were granted a decree nisi in the High Court, reported New York Daily News quoting her friends.
"Charles has been texting and phoning Nigella endlessly. One minute he's pleading, the next bullying. Her silence has been driving him crazy," a source told the newspaper.
Lawson reportedly received a panicked text message from Saatchi's 18-year-old daughter Phoebe too, who expressed concerns about her father's behaviour.