The D.C. auditor suggested yesterday that the city school system could halve its requested $30 million budget increase for 1984 if personnel and supplies were reduced to keep them in line with falling enrollments.

Auditor Otis H. Troupe, who said in a report on the schools' $336.5 million budget request that he was "hindered by a lack of information provided in support of various expenditures," recommended a budget of only $321.5 million.

That amount would be just $3 million more than the $318.5 million budget proposed by Mayor Marion Barry, who is now engaged in a fight with the school board over the budget. Barry's proposal represents a $12 million increase over the current year.

"While most District agencies, in recognition of difficult economic times, must make sacrifices, . . . the Board of Education requests a funding increase that will apparently more than maintain . . . existing service levels," Troupe wrote.

Neither school board President David H. Eaton nor Superintendent Floretta D. McKenzie could be reached for comment.

School officials have privately talked about compromising at a figure no lower than $330 million. Barry said at a press conference yesterday that he is sticking with his budget figure.

Troupe was asked to review the schools' budget request by City Council Chairman David A. Clarke, who has said he would support a budget higher than the mayor's proposal, but only to avoid teacher layoffs.

The schools' budget proposal states that officials expect 88,800 students to be enrolled in the city's schools next year, 3,000 fewer than the current year. Troupe's report points to this decline, which continues a longstanding trend, as a reason for keeping the schools' budget down.

The auditor's report says the schools could save $9.6 million by reducing personnel--teachers and support staff--by 304 positions to 8,756 employes.

Troupe said $1.8 million could be saved by closing 13 schools that McKenzie urged the board to close last year. He said his estimates did not include any money the schools could make by leasing the buildings to private businesses or other city agencies.

Troupe also suggested the board's safety and security budget could be trimmed by $1.4 million, along with $1.7 million for supplies and materials.

Meanwhile yesterday, Clarke said his own review of the schools' budget request suggested the school board had overestimated its full-time, permanent personnel costs by $8.4 million.

Clarke, who is to make his own budget recommendations to the council next Tuesday, is expected to recommend more money than Barry did, but far less than what the board wants.

Clarke held a meeting yesterday with most of the council members to work out final details on his budget submission. The chairmen of eight council committees recommended a total of $25 million more in spending above Barry's $1.9 billion budget.