Engineers have begun studying sites for a proposed underground subway connection between Harvard Square and Porter Square, officials in the Cambridge Planning Commission and the Massachusetts Transit Authority said yesterday.

The engineers are working chiefly along Massachusetts Avenue, planning to run an underground line as far as Porter Square and a surface line westward along this thoroughfare.

The study, directed early in July by the State Legislature, seeks to vastly extend Cambridge's rapid transit system, to replace what one official called "the most expensive surface line in the system." The extension would go as far as Arlington Heights.

Long Considered

According to spokesmen for the MTA, this extension has been under consideration since before 1945. The survey now under way will probably require two-and-one-half months for completion.

Then, officials said, the construction of the extension hinges on two factors: 1) whether the Legislature will approve the recommendations of the engineers; 2) whether it will appropriate sufficient funds for the costly project.

Lands Sought

One spokesman for the Planning Commission said authorities have already begun negotiating for lands to be used for the proposed surface lines. He added that Metropolitan District Commission land west of the Alewife Brook Parkway has been reserved for a transit terminal.

According to one official, an under-ground line costs at least $1,200 a foot, while surface lines cost considerably less.