The Manassas City Council has hired a Harrisonburg architectural firm to draw up building plans for a multimillion-dollar high school.

For two years city officials have debated whether to build a new high school in a decade when surrounding jurisdictions are closing schools. School Board members have argued that enrollment projections show the city's only high school, Osbourn High, will become increasingly crowded by the 1990s unless a new school is constructed.

In early February, the council agreed to build a high school, but did not decide on the details, according to City Manager C. M. Moyer. Now city officials are haggling over the price tag for the new school and its site.

The council is considering two proposals: a $9 million school for grades 10, 11 and 12 or a four-year school that would cost $11 million.

"I don't know when we are going to settle on the price of the school, but I am hoping we can go to bid in 90 days," said Joseph B. Johnson, chairman of the Manassas School Board. "We want to narrow down the sites right away because we are looking to occupy the building by the fall of 1984."

This week the newly hired architectural firm, Davis and Associates, and city public works officials will be inspecting four potential sites for the high school, Johnson said. Their cost estimates for utilities and site improvements "will have an influence on negotiations for the sites," he said.

After the council has settled on how much it will spend, the architect will get a fee amounting to 3 to 5 percent of the total cost of the new building, Johnson said.