Newcastle, 13th in the Premier League on 11 points from nine games, have not commented.
Officers were satisfied the two men were not a threat to the public.
The pair were in a car when officers intervened following the alert.
They were stopped about seven miles from where they were first seen.
Police searched the car and seized a bow and arrows.
It added there was no threat to the public.
Northumbria Police said officers attended and later stopped a vehicle in the Darras Hall area. Reports said six police cars were sent, including armed officers. A police statement said it was understood the items were for recreational use.