The Heritage Foundation wants the Federal Aviation Administration to get out of the air traffic control business and let a private company tell airplanes where to go.

The proposal is one of several transportation initiatives in the conservative think tank's document, "Mandate for Leadership II," which has been distributed to Cabinet members for consideration. A copy of the transportation chapter was obtained by The Washington Post.

The document expresses disappointment in the Reagan administration's stewardship of conservative transportation principles but suggests that it can improve its record in its second term if it will:

*Reduce federal highway taxes and transfer all road-management functions to state and local governments.

*Encourage tolls on many highways and bridges, especially the interstate highway system.

*Stop subsidizing Amtrak, the national passenger train network.

*Provide incentive grants to communities that eliminate the regional monopolies that many local transit systems have, and encourage Transportation Enterprise Zones "in which firms and individuals would be free to offer all transportation services." That way, the document suggests, the presently illegal "gypsy taxi" could become a "legitimate addition to the transportation system," particularly in less-affluent neighborhoods.

*Fully deregulate the partially decontrolled trucking industry and eliminate trucking regulation as a responsibility of the Interstate Commerce Commission.

*Complete the sale of the Consolidated Rail Corp. (Conrail) to private industry.

*Transfer to private control the management of the space shuttle and NASA's planned space station. Veto any legislation that would reregulate transportation. Some railroad reregulation is certain to be a topic for the next Congress.

"Rhetorically, the administration continues to support free-enterprise transportation policies," the foundation said. "In practice, it has surrendered to the traditional belief that all roads start and end in Washington."

The transportation section's authors seem particularly offended by the gasoline tax increase to rebuild highways and bridges that was levied with the full support of the administration during the 1982 lame-duck session of Congress. That increase was "deceptively labeled" as a "user tax," the report said.

Transportation Secretary Elizabeth Hanford Dole has received a copy of the report, and some of its authors have briefed top DOT officials. Most of the proposals have been made before by the Heritage Foundation and other conservative groups; few have made much headway on Capitol Hill.

The proposal to turn the air traffic control system over to the private sector is part of a proposed aviation reform package that the authors see as necessary if airline deregulation is to proceed logically and if the air traffic system is to function at peak efficiency.

As a trial, they proposed that air traffic control functions for an important region of the country, such as the area around Chicago or New York, be placed under a Regional Airspace Management Corporation, which would operate air traffic services as a private business.

The authors suggested that their solutions would help solve the problem that became visible last summer when airlines overscheduled themselves in a way that the air traffic system could not handle without delaying flights. In addition to phasing in private control of FAA radar, computers and employes, the report recommended that the government:

*Sell Washington National and Washington Dulles airports to the highest bidders, at auction.

*Modify future air traffic computers so they can bill airplanes as they use the system. That would end an argument over who is subsidizing whom in air traffic control.

*Permit the sale of takeoff and landing "slots" at busy airports.

*Permit airports to vary landing fees or try other market-based pricing schemes to help them control demand.

* Reduce federal fuel and ticket taxes, freeing revenue for airports.

The FAA already uses the private sector to operate 10 small airport towers, is negotiating for private operators at five more towers and plans in 1985 to add another 30 towers. All are at "visual flight" airports not equipped with radar.

The FAA estimates that it saves $100,000 to $110,000 annually per tower by using private firms. However, the FAA never has favored turning the whole system over to private companies. "We're not planning to do it this year either," a source said yesterday.