The messages have been allegedly sent to the television star, who lives near Dial Post, Horsham, on social media site Twitter, mocking her 14-year-old son Harvey who is blind.
On Twitter she posted a picture with the message “Caught out!! Another bully on our hands. Anyone know this guy??”
She later thanked her followers for their support in the investigation.
A spokesman for Sussex Police said: “Police are aware of offensive social media posts targeting Katie Price’s son and an investigation has begun.”
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