Speaking to the BBC, Jim Morse, a senior director at the authority, said of the projected cost: "I think it's a high probability that in the short term it will undoubtedly go up.
"We've still a lot to discover, we haven't started waste retrieval in those parts of the estate where the degradation and radioactive decay has been at its greatest."
When asked if the cost increases could run into billions of pounds, Mr Morse said: "I'm sure it'll be some billions, I really don't know.
"No-one's done this before. It's very difficult to find another measure. There's nothing in engineering terms that allows you to extrapolate from what you have today."
A pilot project to investigate the task of dismantling has been under way for years at one of the most distinctive landmarks at Sellafield - the giant sphere of the 1950s-era Windscale Advanced Gas-cooled Reactor.
Discovering the extent of Sellafield's nuclear legacy
We were allowed inside - dressed in hard hats and white overalls - passing through a steel corridor into the vast dome of the reactor's containment housing.
Down below us, behind heavy shielding, robotic tools have been used to break up the most contaminated elements which are then extracted and sealed inside giant concrete blocks.
For the moment the blocks - along with all nuclear waste - are stored in temporary facilities while the government decides where and when to build a long-term underground dump.
A spokesman for the Department for Business, Enterprise and Regulatory Reform suggested the government was ready for the clean-up's costs to rise.
"As the NDA continues its work to establish - for the first time - the scale of the challenge, the assessment of the costs involved will naturally need adjusting," he said.
The spokesman also added that the next generation of nuclear power stations would produce less waste than the older ones, and that the power generators would be obliged to pay for the costs.
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