In an effort to reduce the number of midair near-collisions, the Transportation Department plans to announce major new restrictions of private aircraft around nine large U.S. airports, including two in the Washington area, federal and aviation industry sources said yesterday.

The restrictions will prohibit private aircraft that do not have sophisticated communications equipment and permission from air traffic controllers from entering the restricted zones around the airports, known as terminal control areas (TCAs). The additional nine TCAs represent a major increase over existing TCAs at the nation's 23 busiest airports.

The change will be felt acutely in the Washington-Baltimore area because new TCAs will be established around Dulles International and Baltimore-Washington International airports, the sources said. National Airport already has a TCA.

The sources said that the other seven new TCAs will include airports at Orlando and Tampa, Fla.; Phoenix; Salt Lake City; Memphis; Charlotte, N.C., and Hobby Airport in Houston.

The new restrictions are expected to be announced today by Transportation Secretary Elizabeth Hanford Dole.

The Transportation Department also plans to impose new requirements for commercial aircraft to carry collision-avoidance equipment, which warns of impending collision, sources said. The Federal Aviation Administration has said it plans to require installation of the collision-avoidance systems in passenger jets over the next two years.

No airlines currently require the equipment, though Piedmont Airlines has tested it on some jets.

Transportation Department spokesmen did not respond yesterday to requests for comment. Industry sources said it is unclear how quickly the new regulations could be put into effect. They said it is likely the change would have to go through the lengthy federal rule-making process, with extended hearings and periods of public comment.

The department tried to make similar changes in 1978 following the deadly midair collision of a Pacific Southwest Airlines Boeing 727 with a small plane over San Diego. The effort was largely defeated by private pilots, who have fought what they consider to be unnecessary restrictions on airspace.

Concern about midair collisions has been heightened since the August 1986 collision of an Aeromexico Airlines DC9 and a small, single-engine airplane over Cerritos, Calif. And the movement for restrictions has accelerated since the near-collision last week between a single-engine plane and a helicopter carrying President Reagan to his ranch outside Santa Barbara, Calif.

The major target of the new restrictions would be private pilots who often fly without instruments using visual flight rules. Most jets fly on instruments and are under almost continuous supervision of air traffic controllers.

To enter the restricted TCAs, private pilots must have permission from the controllers and aircraft communications equipment, including a radio and a transponder equiped to transmit data on the plane's altitude to controllers.

In sparsely populated parts of the country, it is not uncommon for private pilots to fly with neither a radio nor a transponder.

A TCA occupies a portion of airspace shaped like an upside-down wedding cake. DOT is already attempting to increase the size of all TCAs to extend to an altitude of 12,500 feet with a diameter ranging from 10 miles at the bottom to 60 miles at the top. Up to now, they were smaller and generally reached 7,000 in height.

Under the new rules, most small-aircraft pilots without the proper equipment would not be able to fly over the TCAs in their unpressurized aircraft without carrying supplemental oxygen. Instead, many private pilots who oppose the restrictions say, they will have to fly under and around the edges of the TCA at low altitudes, a practice they say can lead to a congregation of small planes not far from the landing paths of large jets.

Patricia Weil, a private pilot and spokesman for the Aircraft Owners and Pilots Association, a lobbying group for private pilots, complained yesterday that the new TCAs in the Washington-Baltimore area would overlap and create a huge barrier to north-south private aviation traffic along the East Coast.

She said her group is also concerned that the air traffic control system is now working at capacity at the nation's busiest airports.