Disclosing rumors vs. facts during the sale of property

I'm in the process of selling my home in California where I lived for 9 years. During the open house, my broker was approached by a neighbor who lives on the street claiming someone died in my pool before. I think this is a rumor because I checked a report of death and my address is not showing up. I'm currently in escrow with the new buyers and my agent wants to disclose this rumor to the new buyer. I disagree because this is a rumor and not a fact so why disclose it. My question is, do I have to disclose this rumor if there is nothing proving this as a fact?