With less than two weeks left to apply in the competition for $400 million in land and subsidies to build a science and engineering graduate school in New York City, some of the world’s great universities continue to change plans and jockey for position, and there is a growing view among them that Cornell and Stanford have emerged as the favorites.

City officials discourage the idea that there are any front-runners, but the president of Stanford, John L. Hennessy, says bluntly that his school and Cornell — both seeking the same piece of city-owned land on Roosevelt Island — have the best chances, and officials at some of the competing institutions privately agree.

Mayor Michael R. Bloomberg has roiled the field by suggesting lately that he might anoint by year’s end not one winner but two, which has bolstered the hopes of Columbia and New York University, which are both seeking to expand without using the free land the city has offered. But university administrators say they are unsure whether the talk of multiple winners might mean approving two proposals for two separate sites, or forcing a shotgun marriage between competing institutions, and city officials will not say.

With Cornell emphasizing its connections to the city, including its medical school on the Upper East Side, Stanford last week announced an affiliation with City College of New York, and Columbia confirmed that a proposed alliance with City College’s parent, City University of New York, had been dropped.