Lancashire Police launched an investigation after Blackpool supporter Steve Reid alleged a gun had been brandished during an argument he had with Oyston last Thursday outside the club's Bloomfield Road stadium.
Oyston is reported to have been involved in a heated exchange with Reid, who had hand-delivered a letter at the ground.
The police, understood to have viewed CCTV camera footage, have taken no further action and consider the matter closed.
A police statement said: "We received a report of an altercation between two men outside Blackpool Football Club at shortly after 11.30am on Thursday 25 June
An allegation was made that a firearm was brandished during the incident.
"Following a thorough investigation it was established that at no stage was a firearm brandished or used to threaten any other party and no criminal offences were committed.
"However a 48 year old man was spoken to in relation to carrying a firearm in a public place.
"The matter has now been concluded."
Blackpool declined to comment when contacted by Press Association Sport.
Oyston was handed a six-week ban from football and fined £40,000 by the Football Association last month for a text-message exchange in November when he called supporter Stephen Smith "a retard" and told him to "enjoy the rest of your special needs day out".
Blackpool were relegated to Sky Bet League One last season and their final home game against Huddersfield was abandoned after a pitch invasion early in the second half by fans protesting at the way Oyston is running the club.
Source : PA
Source: PA