Previous question, I said gas, I mean oil furance. When the furance shuts off, the fan will run approx 5 minutes, then that will shut off. Approx. four to five minutes later after that shuts off we will hear a chirp from the furance area. What could it be?

crickets :)

It's possible that the fan is hitting something or the bearings are failing. The fan is spinning down during this time.

Don't buy the cricket explanation, but worth a chuckle.