I have checked the tstat and the wiring could it be the relay in the board?

Which type of heating system is it-if it's a Gas Furnace then in a gas furnace the fan is controlled by the system it self.
U can try 1 thing
If system is in off mode and fan in in auto
If fan still runs
Remove the stat off the wall
If fan still runs
Remove G wire out of the terminal
If still fan is running then its your heating system for sure

Also keep in mind sometimes it takes the unit a minute or two to cut off after you switch it to off.

If the unit has a status LED, it may provide a clue as to why the fan is running. Units with this feature usually have a label on the blower access panel or within the blower compartment, with a legend describing the status LED activity.