The state agency that built the Boston Common parking garage hopes to build a similar but smaller structure beneath Cambridge Common.

Sources close to Gov. Peabody's office have reportedly told the agency that Peabody will approve the project. If the garage can be built without destroying the character of the Common or aggravating the Harvard Square traffic problem, neither the City nor the University is expected to oppose it.

Samuel A. Valenti, chairman of the Massachusetts Parking Authority, said yesterday that he would see the Governor "just as soon as I can get an appointment." Peabody will return to the State House sometime tomorrow after a vacation in the Virgin Islands.

Valenti said the garage as currently envisioned would hold 1000 cars and cost $5 million, compared to the Boston Common garage, which has a capacity of 1400 and cost $9.6 million. Although the MPA has not yet prepared plans for the Cambridge structure, Valenti said it might be connected by an underground passage to the Harvard Square MTA station.

"It will probably be a year or two" before the Governor and the Cambridge City Council approve the garage and the state legislature authorizes its construction, according to Valenti. Once work is begun, he said, the garage will take about eight months to build.

While Cambridge and Harvard officials yesterday expresed interest in the garage, they requested further details before commenting on the merits of the plan.

Alan McClennen, director of Cambridge's planning office, said that it would be "very courteous" if the MPA informed the City of its plans, including the location of the garage's entrances and exits. "There is definitely a need for parking space near the Square." McClennen said, "but in dollars and cents it's a lot more complicated."

Charles P. Whitlock, assistant to the President for civie affairs, said that "to build a garage that wouldn't fall in" would probably cost about $10 million rather than $5 million, as the MPA estimated. He added that the University had found that underground parking facilities, such as those at Peabody Terrace, cost $5-10,000 a car space, not $5000.

But financing the garage is not a problem, according to Valenti. He said that one of the reasons the MPA had decided to build its second project in Cambridge was that the funds for construction here were readily available. A national brokerage house has already agreed to underwrite the necesary bond issue, he said.