A private, run-for-profit university has launched an aggressive expansion plan to jointly run at least 10 of its publicly funded counterparts, the Guardian can reveal.

BPP, which offers undergraduate and postgraduate business and law degrees at 14 UK study centres, said it was in talks about managing the business side of the universities' campuses. Talks with three are at a "serious stage", but commercial negotiations are yet to begin.

Under the model, universities would control all academic decisions, while BPP would be responsible for managing the campus estate, IT support, the buying of goods and services and other "back office" roles. BPP would not hold equity in the universities.

Chief executive Carl Lygo said his firm stood to make tens to hundreds of thousands of pounds from working with each institution, but that it would be "too radical at the moment" to bid to take over a university. "The partnership model is more palatable in the UK ... we have a long tradition of higher education being publicly funded, rather than run for profit."

BPP also plans to increase the number of its own undergraduates tenfold by undercutting publicly funded universities next year, when they will be able to charge up to £9,000 a year. At the moment, BPP has just over 1,000 undergraduates. "We want to offer a radical, high-quality alternative, with classroom-hours contact which is in small groups," Lygo said.

BPP's disclosure comes ahead of an imminent white paper expected to signal the government's intention to encourage the expansion of private institutions in higher education in England. Ministers believe they will encourage competition and improve the quality of degree courses.

In an interview with the Guardian last year, David Willetts, the universities minister, said there would be "greater diversity" in the higher education sector in future and that "the crucial thing is for the existing providers to rise to the competitive challenge they will face".

The government hopes private firms will drive down tuition fees, which could save the Treasury millions of pounds.

Many more universities than the government expected intend to charge the maximum of £9,000 a year from autumn 2012. The government pays students' tuition fees in the first instance, and graduates pay them back when they are earning more than £21,000. Higher fees mean the government will have to pay more up front, which may not be sustainable.

BPP would not disclose the names of the universities it is in talks with. Lygo said, however, that they were a "mixed bag" and "not necessarily those who were in financial difficulty".

Universities could save a quarter of their costs if they agreed to BPP running the commercial side of their operation, money they could invest in the academic side, he said.

"We have got a lot of universities in the UK and not all are in a strong financial position ... There is an opportunity for the private sector to help the higher education sector to achieve its goals. By working in partnership, the private provider would add expertise in the back office functions.

"Most universities are running at high costs and don't properly utilise their buildings. The private sector is better at procurement because they are keener at negotiating better prices."

Barclays Corporate, which lends money or provides banking services to 60% of the country's universities, said other large private providers were looking at the UK. "I think what BPP is doing is very indicative of what is happening in the market and indicates the changing environment that universities are operating in," said head of education Chris Hearn.

He added, however, that private firms may be put off by "relatively thin" margins and "heavy regulation". Others may be dissuaded if, unlike BPP, they do not have a base and reputation in the UK.

Roger Brown, professor of higher education policy at Liverpool Hope University, said BPP's plans could make universities more efficient, but ultimately the company's shareholders would be its top priority. "The problem with partnerships is that they blur accountability," he said. "It is unclear who will benefit and who will pay for these partnerships and to whom they are accountable."

Earlier this month, it was announced that the philosopher AC Grayling had set up a private college, staffed by celebrity professors, which would offer degrees in the humanities, economics and law from 2012 at the cost of £18,000 a year.

Other private companies already provide services to universities. The University Partnerships Programme manages student accommodation, while INTO runs courses at UK universities for overseas students who need extra preparation to get onto degree programmes.

Last July, BPP was given degree-awarding powers, which meant it was allowed to call itself a university college. It was the first new private university in the UK for more than 30 years. Willetts said it was "healthy to have a vibrant private sector working alongside our more traditional universities". This would create a "dynamic and flexible" degree system and could encourage online degrees, he said.

BPP is part of the Apollo Group, a market-listed US company that owns the University of Phoenix, a private institution offering degrees through distance learning. In 2004, Phoenix was fined $9.8m (£6m) for unethical practices in recruiting students.