Dame Julia King, head of Aston University, made the comments during a debate with other vice-chancellors and sector representatives at the Festival of Education, held at Wellington College in Berkshire on 23 and 24 June.
"Personally, despite running a UK university - and I clearly would like the best UK students to come to us - I actually think we should be encouraging our 18- and 19-year-olds to think about going abroad," she said.
"The Western world is no longer the economic centre of the globe: we have to be much more competitive with the rapidly growing Asian economies."
She added that there were "thousands" of Chinese, Indian, Korean and Vietnamese students coming to the UK, but asked why British students were not going to China.
"That's something I think we need to help and encourage our young people to do," she said.
The panel member of the 2010 Browne Review added that links forged between UK and international universities, and the "good value" for money of some European institutions, meant overseas study was increasingly attractive.
She said: "Many of our European colleagues are now teaching courses in English, and just at the moment they are very good value - although given the economic situation in Europe, I think we'll very soon see all of our European colleagues going down a very similar path on fees to the one we've taken in the UK."
But Terence Kealey, vice-chancellor of the University of Buckingham, said that UK universities were better than their European counterparts because of their autonomy and that over the next decade they would supplant US institutions as the "best universities in the world per capita".
"Our universities are hugely better [than those on the Continent] simply because the English-speaking world has a tradition of university autonomy," he said. "The rest of the world has the Napoleonic tradition of the universities as branches of the Civil Service."