Does your furnace have a spark ignition system, that makes a ticking sound at start up before the blower comes on? If so the clicking may be the flame rectification system on the spark ignitor. If your system as a hot surface ignitor this would not apply.

Try turning the fan in the fan on position, and have the heat selector in off. If the clicking noise starts, there could be paper or other materials in the blower housing, or the bearings on the blower may be going out. If so, turn off the power from the unit, unplug the blower motor wires, ( Note where they go) then remove the two screws holding the blower motor housing and the housing should slide out, then you can take a flash light or other device and look inside the blower housing. If no obstruction try rotating the Blower blade by hand and see if you can hear the clicking noise. My bet is that its an obstruction in the blower housing or that there is a flame rectification problem...