The offer was made last month by Gers chiefs as part of efforts to reduce the risk of disturbances like those sparked amid celebrations when the side won the title in March.
It is understood the proposal would also have seen four more title parties held in the days after, each hosting another 10,000 season-ticket holders.
However, their offer was rejected by Holyrood officials due to Covid-19 rules which banned mass gatherings at that point.
An estimated 15,000 fans descended on Ibrox and Glasgow's George Square, on Saturday with fresh scenes of disorder taking place - including reports of fighting, public drunkenness and sectarian chanting.
In the letter sent to a high-ranking official on April 21, Rangers chief executive Stewart Robertson said: "I'd be grateful if you could explore the possibility of us allowing some supporters into the stadium when we play Aberdeen on Saturday the 15th of May.
"As you know we are keen to ensure that we minimise the risk of crowds gathering outside the stadium or in other areas of Glasgow and Scotland on the day.
"We believe that we can have a better chance to achieve this if we were to be allowed to have fans in Ibrox Stadium to attend not only the match on May 15 but also on the days following the match when we could have players at the stadium to parade the trophy within the stadium."
The proposal would also have seen four more title parties held in the days after, each hosting another 10,000 season-ticket holders.
However, the official rejected the proposals in a letter sent on April 27.
It said: "While we are making encouraging progress in suppressing the virus, we cannot jeopardise this with mass gatherings in breach of Covid-19 regulations and public health advice.
"As you know, we are cautiously relaxing the restrictions which have been helping to keep people safe.
"From Monday May 17 - the next significant relaxation of restrictions in Scotland - limited numbers of supporters will be allowed to attend football matches in areas with level 2, 1 or 0 restrictions. We expect the whole of Scotland to go into level 2 on that date.
"Unfortunately, no supporters will be permitted to attend any fixtures before that date. I realise that is disappointing in relation to your proposals for May 15."
The Aberdeen game had been due to take place just two days before most of Scotland moved into Tier 2 conditions, under which crowds of up to 500 were permitted, with event organisers able to apply for an increase.
Five police officers were injured in Saturday's scenes and 28 arrests were made.
Scotland's First Minister Nicola Sturgeon condemned the actions of those responsible as she hit out at the "disgraceful scenes".
Tweeting on Sunday, she wrote: "To say I'm utterly disgusted by the Rangers fans who rampaged through the city would be an understatement."