Former Hearts striker John Robertson said the plea was made at half-time during a game against Hibernian at Easter Road in September 1990.
Police had been struggling to control the crowd at the game as Hearts took a 3-0 lead in the first half.
The story emerged in a BBC Scotland documentary on Scottish football.
The four-part series traces the last 30 years of the sport in Scotland.
The opening programme, I Play for Money, looks at how ambition and financial pressures left some clubs vulnerable to takeover or collapse during a turbulent period in the game.
In the run-up the 1990 Edinburgh derby, Hearts chairman Wallace Mercer had attempted to buy Hibernian from David Duff - a solicitor who had acquired the Easter Road side, and who was later imprisoned for fraud offences in England.
Mr Mercer's takeover bid sparked an ultimately successful campaign by Hibs fans to thwart the deal, but feelings were running high and spilled into trouble at the match.
Mr Robertson told the BBC: "The place was packed to the rafters, and it was a horrible atmosphere. Hibs fans were going bananas and rightly so, Hearts fans weren't too happy about it either.
"We were the anti-Christ at the time, we were the enemies."
He said that a senior police officer had came into the dressing room at half-time with other officers and told players: ''We fear another pitch invasion, you know, we're going to basically say if you score another goal and Hibs fans invade, we may have to stop the game, so you know, if you can help it, don't score.''
Mr Robertson added: "We were all looking stunned, thinking - some strange request, that.
"He went out the door and Sandy Clark [Hearts caretaker manager] said 'Yeah, yeah officer, no problem at all, no worries, I know where you're coming from, we'll leave it at that.'
"He shut the door and said: 'Nah, that ain't happening guys.'"
However, Hearts failed to find the net in the second half and the score remained 3-0.
Rod Petrie, current chairman of Hibs, reflected on the significance of the Hibs fans' campaign.
He told the documentary: "It was probably close to the club's darkest hour and everybody who was part of Hands Off Hibs deserves great credit for the passion that they showed and the determination they showed to save the football club."
Hearts supporter Alex Salmond, MP, said: "Anybody who really understands football understands that you can't have yin without yang.
"You can't have Hearts without Hibs, you can't have Celtic without Rangers and you cannot, must not, ever effectively deprive people of their football loyalties."
The first episode of Scotland's Game is on BBC One Scotland at 21:00 on Thursday 25 August.
A senior officer policing a heated derby match urged the winning team not to score again because he feared a pitch invasion, an ex-player has said.