The federal government will probably approve in the next few weeks a low bid for the construction of the new Harvard Square subway station despite the fact the bid is 40 per cent above the estimate provided by a local consulting firm.

The Massachusetts Bay Transportation Authority (MBTA) board of directors has already approved the $71.3 million bid, submitted by the Perini Corporation of Framingham, Mass. The Urban Mass Transportation Authority (UMTA) must finalize the award of the federally-funded contract.

A spokesman for Cambridge Mayor Thomas W. Danehy said yesterday the mayor is afraid the increased price of the project, which the MBTA's consulting engineers estimated would cost $50.3 million, would soak up funds that otherwise might have been available for further extension of the Red Line beyond Cambridge.

UMTA has already granted nearly $200 million of a total of a half a billion dollars for the extension of the Red Line to the Alewife Brook Parkway.

MBTA spokesman Vincent B. Farrell said the Mayor's fears are "pure conjecture."

Changes in operating procedures and fears of future inflation drove the cost of the contract up, farrell said.

Warren J. Higgens, MBTA director of construction, said last week his office will scrutinize the bids carefully before it asks UMTA for final approval.

"The most important factor is the demolition required," he said, adding, "Many thousands of feet of concrete structure will have to be removed under stringent conditions."

Construction of the new Harvard Square station and the temporary Harvard Holyoke station may begin as early as next spring, spokesmen in City Hall said yesterday.

Perini Corporation employees refused comment yesterday on the increased costs of the project.

A meeting between the MBTA board of directors, city officials and Cambridge citizen representatives is tentatively scheduled for tomorrow