WASHINGTON (AP) _ The Pentagon is planning long-term support for Navy forces in the Persian Gulf, following the rapid buildup that has put more than 20 U.S. warships there and in the nearby Arabian Sea.

Officials said Friday that the Joint Chiefs of Staff have asked the Navy to explore the possibility of establishing floating supply stations for mine- sweeping operations in the gulf.

The officials, who asked not to be identified, said the request was part of a logistics planning effort focusing on long-term support for American forces in the gulf.

The Reagan administration has said it intends to help protect Kuwaiti oil tankers plying the waterway as long as there is a threat of attack by Iran. Kuwait is a key ally of Iraq, which is engaged in a 7-year-old war with Iran.

Figures obtained from the Pentagon on Friday give an indication of the size of the U.S. commitment, showing that more than 10,000 U.S. servicemen will receive ''imminent danger'' pay bonuses for service there.

In June, before the Reagan administration's decision to escort the Kuwaiti tankers, only 160 American servicemen around the world were receiving the $110-a-month payments, and they were spread among five different countries.

According to the sources, the joint chiefs want to determine if barges could be leased and anchored in the gulf to store food, fuel and other equipment needed by mine-sweeping boats operating in the gulf.

The Navy used such floating base camps in rivers during the Vietnam war.

An amphibious cargo ship, the USS St. Louis, sailed into the gulf earlier this week bearing two small mine-sweeping boats. Another amphibious vessel, the USS Raleigh, is near the gulf with four mine-sweeping boats aboard.

The St. Louis and the Raleigh are part of the 12-ship Middle East Task Force operating in the gulf itself. The 10-ship Constellation battle group is deployed nearby in the Arabian Sea.

In addition, the Pentagon has ordered six larger mine-sfind some way to support the mine-sweeping boats without maintaining large amphibious ships nearby. They stressed, however, that it was too early to say whether the suggestion of using barges would be adopted.

The Navy so far has conducted five convoy operations. With the exception of the first in July, during which the tanker Bridgeton struck a mine, the tankers receiving escorts have made the journey successfully.

The officials said another convoy operation would be mounted soon, but they refused to elaborate.

Meanwhile, a battle group led by the battleship Missouri is heading for the northern Arabian Sea. The battleship force is expected to arrive in the area by Sunday or Monday, the officials said.

The battleship probably will be ordered soon into the Gulf of Oman, closer to the Strait of Hormuz, to help shadow convoys traversing the gulf's sole entrance, they said.

Pentagon figures show that the Reagan administration's decision to authorize ''imminent danger'' bonus pay for U.S. military personnel in the gulf region is by far the largest such commitment since the payments were authorized in 1983.

The estimated 10,000 qualifying military personnel in the Persian Gulf region will receive the danger payments starting this month.

According to statistics obtained Friday from the Pentagon, more than 13,600 servicemen received the danger payments at some point in 1983. That total was swollen by payments to the forces who participated in the invasion of Grenada and to the Marines who were stationed in Lebanon on a peacekeeping mission.

The payments to 8,765 servicemen involved in the Grenada operation lasted only three months, and the Marine force in Lebanon was withdrawn in February 1984.