A discussion paper, published by John Swinney, the Scottish finance minister, examined the case for the creation of an oil fund into which the money would be paid and saved.
However, it admitted that Scotland already gets a share of the tax take from gas and oil as part of its annual block grant from Westminster each year.
Mr Swinney argued that an oil fund would secure billions of pounds extra for Scotland each year.
But, for this to happen, the paper said a deal would have to be struck with the Treasury that the extra money would not lead to an equivalent reduction in the block grant.
This would effectively mean Scotland receiving some North Sea tax revenue twice.
The paper also admitted that during the current recession ministers could only afford to put money into the fund by cutting public spending, raising taxes or increasing borrowing.
Andy Kerr, Scottish Labour finance spokesman, accused Mr Swinney of "trying to have his cake and eat it."
He said: "This is just a financial fairyland designed to create a fight with the rest of the UK.
"The real failure of his thinking is set out in the document where he admits that for his plan to work, he wants to use the money from an oil fund on top the block grant. He's trying to spend the same money twice."
About 40 billion barrels have been extracted since drilling began in 1967, the paper said, producing £269 billion in receipts of the UK Exchequer.
However, an estimated 15billion to 25 billion barrels of oil remain, and it is estimated that the sector will generate £45 billion of tax revenue in 2008-09.
Oil funds have been established in Norway, now worth over £200 billion, as well as Alberta, worth £8 billion, and Alaska, worth £19 billion.
The paper admitted that in only six financial years since 1980-81 have the UK's finance's been in surplus, meaning the rest of the time spending has exceeded tax revenue.
It said North Sea tax revenue has been spent by successive Governments "to fund public spending and to reduce taxation across the UK."
David Lonsdale, assistant director of CBI Scotland, said Mr Swinney had to answer: "If this money is being diverted into an oil fund, where is the money going to come from and what is not going to be spent on?"
But the Scottish finance minister insisted that the UK is "practically alone" among oil and gas producers in not having such a fund.
Mr Swinney argued: "The UK Government has without doubt wasted billions of pounds of Scottish North Sea revenue.
"An oil fund is strongly in Scotland's long-term economic interest and the UK Government can no longer oppose the people of Scotland enjoying the oil legacy they are entitled to."