America's large cities will soon need the white suburbs to relieve their segregated and overcrowded schools, a growing number of Harvard educators predict.

They point to projections that whites will continue to leave the cities in large numbers for at least another decade. And the conclusion--that the cities are growing less and less capable of desegregating their own schools--has won wide agreement here during the past few months:

At a Harvard conference on metropolitan education last week, every speaker emphasized that cities and suburbs will have to cooperate to solve the cities' school problems. "Political boundaries shouldn't inhibit us," said Vincent F. Conroy, director of the Center for Field Studies of the Graduate School of Education. "We have to challenge the private-school aspect of suburban schools."

The Center for Field Studies, in a major report to the Hartford, Conn. Board of Education, has urged that Hartford bus 6000 students to nearby suburban schools by 1974. This would be more than a third of the non-white students living in the city, according to Center estimates.

A paper submitted by Thomas F. Pettigrew, associate professor of Social Psychology, to the White House Conference on Education last summer found an "urgent need for suburban involvement in inner city desegregation plans."

Pettigrew's report sums up the cities' quandary. "For 950 years," he told the conference. "Negro Americans have learned that separate facilities for them almost always mean inferior facilities...Many whites, unfortunately, reveal a strong interest in the education of Negroes only when Negroes are found in the same schools with sufficiently large numbers of whites."

Better schools and new teaching methods are both needed by the cities, Pettigrew emphasized. But he went on, "Desegregation and educational upgrading cannot long remain the sole responsibility of inner school systems, even when bolstered by federal and state subsidies. In some cases, the central city is beginning to run out.

The cities and suburbs are approaching timidly the possibility of a joint attack on segregation. "The suburbs have been delinquent," Pettigrew said this week. "They were as responsible for Watts as anyone."

Last week, the Hartford Superintendent of Schools proposed discarding the Harvard plan and substituting "a modest experiment." And in Boston, although 13 suburbs have formed a committee to study busing students from the city, the School Committee has not yet officially decided whether the matter belongs on its agenda.

But educators here--even those who emphasize the need for improvements within the city--are giving more and more support to planning that would include the suburbs.

"I live in South Boston," Thomas Sullivan, a research associate at the Ed School and a former Boston council-man told the participants in the Harvard conference last week. "I know your brothers in the suburbs and I know my brothers. If I had to choose who was better suited to make a new home for the Negro, I'd say yours."