Downing Street said designating Trident's Faslane base as sovereign British territory in the event of a yes to independence was "not credible".
The prime minister's office reacted to reports that the Ministry of Defence had been looking at the idea.
The Scottish government's SNP administration has always said that if independence happened it would remove nuclear weapons from the Clyde base.
The people of Scotland are going to be voting in an independence referendum.
On 18 September, 2014, the electorate will be asked the yes/no question: "Should Scotland be an independent country?"
Reports in the Guardian newspaper on Thursday suggested the UK government could give Faslane - where 6,000 people are employed - a status similar to that of British military bases in Cyprus, designated as sovereign territory.
The newspaper suggested the move would be designed to maintain access for the Trident fleet to the open seas via the Firth of Clyde.
A Downing Street spokesman said such a plan was not "credible or sensible".
He added that no such idea had come to the defence secretary or the prime minister and would not be supported by them if they did.
An MoD spokesman said it was confident Scotland would remain part of the UK and that the scale and cost of relocating the base in the event of a yes vote would be "enormous".
However, a defence source said: "It would cost a huge amount of money, running into tens of billions of pounds, to decommission Faslane.
"Those costs would be factored into any negotiations on an independence settlement. The sovereign base area is an option. It is an interesting idea because the costs of moving out of Faslane are eye-wateringly high."
Reacting to the Guardian story, Scotland's Deputy First Minister Nicola Sturgeon accused the UK government of making an "outrageous attempt at bullying".
In an interview with BBC Radio Scotland's Good Morning Scotland programme, she said: "I cannot see how they could do this without the agreement of the Scottish government - and speaking for my party that is not an agreement which would be forthcoming.
"We want to see Trident gone from Scotland because these weapons are immoral, they are also not needed."
Ms Sturgeon also reiterated the SNP's "principled policy" of getting rid of Trident if Scotland was to become an independent country.
She insisted that removing nuclear weapons from Clyde waters would not be used as a bargaining chip in post-independence discussions with the UK government.
However, she urged ministers at Westminster to engage in "sensible discussions" about Scotland's Future ahead of next year's historic vote.