The 800-year-old institution fears that unless it attracts the world's best students it will not complete with the better-funded Ivy League institutions in the United States.
"We have to fight very hard to keep our position in the world league table to stay up there with Harvard, Yale, Princeton, Stanford and MIT [Massachusetts Institute of Technology]," Lord Patten said.
During a week-long visit to India, Lord Patten will attempt to raise Oxford's profile in Delhi, Bombay and Bangalore. He will meet Oxford alumni, speak at a Said Business School seminar, and meet business leaders to discuss ways of raising funds to provide bursaries for Indian students.
Only 133 of Oxford's 17,700 students are from India, compared to 547 from China.
Lord Patten fears that many bright students are put off by Oxford's "stuffy image", and choose instead to study in the US. About 17,000 Indian students have chosen British universities compared to nearly 80,000 in the US, he said.
"One of the problems in India is that we have a rather conservative, stuffy image. People do not realise the flexibility and modernity of our courses," Lord Patten said. Warning of a crisis in higher education, he added: "We are falling further behind the US." India was a relatively untapped source of talent.
Foreign students are attractive to universities because they pay higher fees than candidates from the United Kingdom. At Oxford, overseas students pay between £8,500 and £11,300 a year compared with £3,000 paid by students from the UK and Europe.
Oxford claims it loses up to £8,000 per student per year, because the cost of running an undergraduate course is about £13,600. The introduction of "top-up" fees will cut the loss by £1,000.
A university spokeswoman said the plan to recruit more foreign students was not a drive to boost Oxford's fee income. But she admitted it was difficult to compete with wealthy American universities which offered generous bursaries.Reuse content