Chelsea College of Art and Design is awaiting news of its bid for the former Royal Army Medical College at Millbank.
Representatives of the London Institute, of which Chelsea is part, discussed their proposals at the Ministry of Defence last week.
Don Gratton, pro-rector of the institute, said the hearing had been favourable, despite fears that private developers looking to transform the listed three-acre site into luxury apartments will be able to offer a higher price.
He said: "We have the opportunity to create an exciting synergy by locating a great art college next to one of the world's greatest art galleries (Tate Britain)."
Mr Gratton admitted that Chelsea's final offer "was not a million miles away" from the rumoured Pounds 30 million asking price. The sum will be raised in part by the eventual sale of the college's four existing buildings.