We have a gas furnace, after the furance shuts off, the fan will run for approx. five more minutes, then that will shut off. Approx. four or five more minutes later we will hear a chirp come from the furance area. We have had the blower check out. Furance company says it is the cooling of the ducting... we don't think so. What could it be?

I have that too. I don't worry about it. As long as my furnace works, chirping or not. It is the duct work cooling off after the hot air going through.