The proposal would also have seen four more title parties held in the days after, each hosting another 10,000 season-ticket holders.
Rangers said their plan was designed to “minimise the risk of crowds gathering outside the stadium”.
But the “concession” on the level three ban on crowds was denied.
On the day, an estimated 15,000 fans choose to descend on Ibrox and Glasgow’s George Square, with 28 arrests and the promise of more to come from Police Scotland after ugly scenes of disorder.
The 4-0 win over Aberdeen took place two days before most of Scotland moved into level two conditions, under which crowds of up to 500 are permitted, with event organisers able to apply for an increase. On Friday, it was announced that Glasgow was to stay at level three due to a spike in coronavirus cases.
Rangers chief executive Stewart Robertson made the request in a letter sent on 21 April.
He said the proposal would “allow us to send a very positive and strong message to our supporters that only those with access on the particular day should be in the vicinity of the stadium”.
He described it as “a common sense, pragmatic way to minimise the number of people who will come out to celebrate the trophy presentation”.
The government reply, dated 27 April, said: “While we are making encouraging progress in suppressing the virus, we cannot jeopardise this with mass gatherings in breach of Covid regulations and public health advice.”
‘Not right to make an exception for football fans’
And a government spokesperson told BBC Scotland: “At a time when people have missed funerals, not seen loved ones in care homes and postponed weddings, it is not right that we make an exception to the rules for football fans.
“We also received advice that there was an increased likelihood that large numbers of supporters would gather outside the stadium if they knew some were permitted inside.
“Despite our clear public messages and continued work with the club calling on fans not to gather illegally in large numbers, the selfish and irresponsible behaviour seen on Saturday endangered the lives of others – supporters, the police on duty and the wider community.”
Meanwhile, Rangers have been urged to take “strong action” against fans who broke the law on Saturday by Justice Secretary Humza Yousaf.
“I’m disappointed on many levels,” said Mr Yousaf. With the selfishness of Covid breaches but perhaps more so with the violence and vandalism we saw on George Square and the anti-Catholic bigotry we saw on display.
“Rangers are working closely with Police Scotland to identify any supporters who are involved in criminal activity and I would urge Rangers to take strong action against any fan who is found to have broken the law.”
‘Strict liability is one of the options’
Mr Yousaf was responding to questions in the Scottish Parliament from James Dornan MSP, who asked about the potential of introducing strict liability, where clubs would be held accountable for the actions of their supporters.
“In fairness to Rangers Football Club, they have engaged for a number of weeks with Police Scotland, the Scottish government and Glasgow City Council, and they released a statement pleading with their fans to respect the Covid guidelines,” said Mr Yousaf.
“What I would say is that I would have liked that messaging to probably have been more explicit and stronger, but nonetheless that messaging did come forth.”
He added: “I think it’s important to engage with the clubs, it’s important to try and bring the clubs forward with us on this journey instead of trying to impose measures upon them.
“But ultimately that is what we may have to do if the clubs are unwilling to acknowledge, unwilling to accept, unwilling to confront the fact that there is a problem amongst some fans then of course we may have to work together as a chamber and as a parliament to find a solution that is appropriate.
“Strict liability is one of the options, and it is one that should remain firmly on the table.”