The messages, posted on Twitter, included one particularly nasty threat: "That b---- is getting cut if David and Posh split."
“When she saw the messages she straight away wanted to protect herself by getting police involved," a source told The Sun.
On Friday, the singer/Dancing With The Stars contestant responded to apparent rumours that she'd had an affair with David Beckham (rumours which no one had actually heard before she tweeted about them!)
“I’ve read some horrible rumours on here and want you to know I absolutely deny I’ve had an affair with David
Beckham," Katherine wrote.
“The rumours are hurtful, untrue and, my lawyers tell me, actionable.”
A rep for the 32-year-old confirmed, "Due to the serious nature of the threats, the tweets have been reported to the police."