Yale president Richard Levin says competition from Asian universities is desirable. Photograph: Graeme Robertson

China's top universities could soon rival Oxford, Cambridge and the Ivy League, the president of Yale University has warned.

Professor Richard Levin, speaking to the Guardian on a trip to the UK, said Chinese institutions would rank in the world's top 10 universities in 25 years' time, squeezing out some of the west's elite campuses.

At the moment, British universities dominate the top 10 rankings, with Cambridge coming second to Harvard, University College London fourth and Oxford and Imperial College London joint fifth. The rest of the top 15 are US universities. China's highest-ranking institution is Tsinghua, at 49.

But the Chinese government now spends billions of yuan �C at least 1.5% of its gross domestic product �C on higher education with the aim of propelling its best institutions, such as the universities of Tsinghua and Peking, into the top slots, Levin said.

"In 25 years, only a generation's time, these universities could rival the Ivy League," said Levin, the Ivy League's longest-tenured president. He was speaking before giving a lecture on the rise of Asia's universities to the Royal Society in London on Monday evening.

Levin said: "China and India ... seek to expand the capacity of their systems of higher education ... and aspire simultaneously to create a limited number of world-class universities to take their places among the best. This is an audacious agenda, but China, in particular, has the will and resources that make it feasible. It has built the largest higher education sector in the world in merely a decade."

China has more than doubled the number of its higher education institutions in the last decade from 1,022 to 2,263. More than 5 million Chinese students enrol on degree courses now, compared to 1 million in 1997.

Chinese scholars are increasingly leaving their posts in US and UK universities to return home, Levin said.

The growth of Chinese higher education comes as English university leaders fear they may not be able to maintain their world-class reputation for higher education, with savage government cuts of £950m over the next three years.

Commenting on the cuts, Levin said it would be "a shame if the British government didn't recognise the status of Oxford and Cambridge as global leaders".

He pointed out that it had taken centuries for Harvard and Yale to match Oxford and Cambridge. And while China had a large pool of talent to draw on, it was currently seen as less attractive to scholars from across the world than the US and the UK, he said. China's universities lack "multidisciplinary breadth" and "the cultivation of critical thinking".

Levin said: "I don't see the rise of Asia's universities as threatening. Competition in education is a positive sum game. Increasing the quality of education around the world translates into better informed and more productive citizens."

He said Oxford and Cambridge's esteemed tutorial system, whereby one or two students have a private class with a lecturer, was "almost unthinkably labour-intensive in an Asian context". Too many academic grants were still given to Chinese scholars because of their political affiliations, Levin hinted.

"To create world-class capacity in research, resources must not only be abundant, they must also be allocated on the basis of scholarly and scientific merit, rather than on the basis of seniority or political influence. To create world-class capacity in education, [China's] curriculum must be broadened and pedagogy transformed." But, he said, these were problems that could be solved with sufficient leadership and political will.