As well as "big cuts" to the Science Museum in London, the group's director Ian Blatchford said one of its outposts in Manchester, York or Bradford could close its doors.
Mr Blatchford said the prospect of a further 10% extra cut in funding meant "almost certainly" that one of the museums would have to go. The group runs the Museum of Science and Industry in Manchester, the National Railway Museum in York and Bradford's National Media Museum.
He told BBC Radio 4's World at One: "There are two problems. The first is we are already in quite a weak position because in the existing spending round we ended up with a 25% real-terms cuts.
"But the real problem is there seems a very strong prospect of a further 10% of cuts, which basically means that we will end up with a deficit, currently of £2 million, rising to about £6 million a year which for a museum is a huge amount of money."
Asked if that would mean the closure of a museum, he said: "I have to say, with a very heavy heart, it really does. We have done lots of boring and sensible things, awful things like cutting staff, procurement, raising more money.
National museums do not charge for admission, but Mr Blatchford said he was in talks with the Government about the possibility of reinstating entry fees. He added: "Even though it might be an option, it's certainly not an option on the table at the moment, I just don't have the power to do it.
"It's part of the conversation we are having with them because, clearly, we appreciate times are tough and they also do appreciate that if the cuts are significant there will be some pain."
A Department for Culture, Media and Sport spokesman said: "It would be inappropriate to speculate on the outcome of the Spending Review. This is an operational matter for the Science Museum Group who has to address a large projected operating deficit from 2014 onwards and is assessing a range of options to address this situation".