The 16 large research-intensive universities that form Universitas 21 are planning to expand membership.
At its annual meeting in Montreal, U21 organisers said they would like to add seven members, three each from western Europe and the US and one from Japan, areas with sparse representation. Only one US institution, the University of Michigan, is a member and there is no European institution outside the UK.
U21 secretary Chris Robinson did not want to reveal the names of universities his organisation plans to accept into the group.
But Oxford, Cambridge and the Ivy League US universities are unlikely to be on the list. One university head, commenting on the make-up of the group, said some of the most prestigious universities may not have the humility to work co-operatively with the U21 universities.
Bernard Shapiro, principal of McGill University in Montreal, said: "You have to believe that someone else has a lot to offer." Dr Shapiro agreed there were no major prestigious institutions in membership yet but said that did not take away from the power of the group, which, he said, "understands the future".
U21 has said it would like not to exceed 25 members. Twenty to 30 universities have made applications for membership at $25,000 a year. Stanford was invited to join last year but has not replied. Most vice-chancellors said the small nature of the group has been a selling point.