Benayoun wrote Monday on Twitter that there are "some ... issues that the club is taking care and try to handle them in the right way..as sometimes people are crossing the limit."
Some British media are reporting that the abuse targeting the Israel international is anti-semitic.
Chelsea hasn't made an official comment.
Benayoun, who was jeered by Chelsea fans when he came on as a substitute against former club Liverpool on Sunday, has been targeted since he gave an interview supporting Fernando Torres in February.
Benayoun is coming to the end of his contract at Chelsea.