Student unions were previously classified as exempt charities, but now have to register with the Charity Commission if they have an income above £100,000.
According to the NUS, some of the members of the elite Russell Group of 20 top universities have told student unions they also have the choice of becoming a department of the university and encouraged them to do so.
"We are aware that some institutions have attempted to use the act to attempt to integrate the students' union into their structures," said Gemma Tumelty, national president of the NUS.
Umbrella body Universities UK said that if a union wanted to retain exempt status it would have to "become more constitutionally integrated with its university", but added that it knew of no university that wanted to impose this approach.
Matt Hyde, chief executive of the NUS, said: "As a campaigning organisation, your ability to represent the rights of your student members independently is clearly annulled if you're a department of an institution."
According to legal advice given to the union, it is doubtful whether the Education Act 1944 would allow a student union to become part of its parent university.
"This confirmed what we believed - that certain registrars have been making these overtures without justification," said Tumelty.
Hyde said some universities were keen to reduce the independence of student unions. "This is a part of the institution they can't control, but which might be a crucial part of marketing to future students in a fees environment," he said.
Jonathan Anelay, director of legal services at Oxford University, which is in the Russell Group, said the union was making irresponsible claims.
"At Oxford, we having a relaxed, consensual discussion with our student union over what is the best course of action," he said.
"It is theoretically possible - although I don't think it is the right thing for us to do - for a student union that is not simply a budgetary unit, like the department of physics, to become one. But I think that is very difficult because student unions need a degree of independence."
Tony Blair will this week announce plans to introduce match funding for donations to universities. For every £2 donated, the Government will give £1. The move brings the UK into line with the US: Harvard last year received $595m (£306m) in donations. The scheme will apply to all English universities. A spokeswoman for Number 10 said: "After higher education reforms, this is the logical next step."