Dean Wood, 21, from Sauchie, has been missing since the incident on the Clackmannanshire Bridge on 13 November.
Police said a member of the public found a body on the riverbank near Inch of Ferryton Farm at 12:00 on Friday.
The body has not been formally identified, but police officers have been in touch with Mr Wood's family.
The incident in November occurred after officers in an armed response vehicle spotted a blue Transit van that was being driven with three wheels on the Clackmannanshire Bridge.
When they signalled to the driver to stop, he crashed the van into a barrier on the bridge.
He then got out and climbed over the bridge's safety railings before entering the River Forth.
A Police Scotland spokesman said: "Inquiries are ongoing to ascertain the identity of the deceased, however, police liaison officers have been in contact with the family of missing man Dean Wood as part of that ongoing investigation."
A body has been found in the search for a man who fell into the River Forth after police officers tried to stop his van.