The Reagan administration is seriously concerned about reports that Israel may send ground forces into southern Lebanon against the Palestinians at the same time the Israeli air force goes into action against Syrian antiaircraft missiles in northern Lebanon.

Such a double-barreled Israeli strike, in the opinion of officials here, would add a new dimension of danger to a Middle East situation already fraught with risk of escalation.

A renewed military conflict in Lebanon involving Israeli, Syrian and Christian forces -- and especially one that extends the battle at the same time to Palestinian forces in southern Lebanon -- could resound through the Arab world, endangering the Middle East peace process as well as the U.S. strategy of establishing new security arrangements with moderate Arab states, according to administration sources.

Presidential envoy Philip C. Habib, who was in Jerusalem yesterday, is seeking a formula for political and military concessions by forces on various sides in order to prevent a new out-break of military action.

Senior administration officials still consider it a long shot that Habib can produce a compromise solution along the lines the United States is suggesting. But because of the high stakes involved and the belief Habib may somehow be able to find new room for maneuver, Washington has determined to continue the search for a peaceful solution.

Secretary of State Alexander M. Haig Jr., after briefing the House Foreign Affairs Committee yesterday, said he is "never resigned" to the possibility of a new war in the Middle East. "I think it is a task of all the parties involved to use every ounce of energy left to prevent the resort to force," Haig told reporters.

Haig added that "it's too early to say" if the Habib peace mission will succeed.

The potential compromise under discussion by Habib with the Syrians, Israelis, Lebanese government and Lebanese Christians is reliably reported to include at least four elements:

Replacement of the Christian militia forces in the Lebanese city of Zahle by Lebanese government troops, providing a basis for ending the siege of that city by the Syrians.

Withdrawal of Syrian forces from the heights of Mount Sanin overlooking Zahle and the Bekaa Valley.

Understandings about future operational practices in the area. Syria has complained about frequent Israeli overflights, and Israel has expressed concern about Syrian troop movements. But the ground rules for military operations in Lebanon have been imprecise and often contested.

Withdrawal of Syrian antiaircraft missiles, apparently with the facesaving rationale that due to negotiated changes, they are no longer needed.

Such arrangements would provide a powerful argument within Israel against the military action that Prime Minister Menachem Begin has threatened in view of "unacceptable" changes in Syrian military deployments, especially the surface-to-air missiles.

Begin told the Israeli Knesset, or parliament, Monday that Syria has increased the number of its antiaircraft missile batteries in Lebanon in recent days. Haig confirmed this yesterday, saying that "very clearly, there has been a thickening" of the surface-to-air missiles in the area as well as "military posturing on both sides."

There is little doubt in the high ranks of the administration that the Israelis could prevail easily in a bid to knock out the Syrian missiles. Of far more serious concern is what could accompany such an Israeli strike, and what might happen next.

Some Israeli advocates of strong military action, according to reports reaching Washington, are discussing ground attacks in southern Lebanon to accompany air forces strikes against Syrian missiles to the north.

A potential objective of such a strike would be to extend the area controlled by the Israeli-backed militia of Maj. Saad Haddad. A more limited objective could be punishment of the Palestinian forces and temporary respite from rocket attacks against Israeli territory.

An Israeli attack on the Syrian surface-to-air missiles could bring a degree of Arab unity behind the Syrians, who have not been in the Arab mainstream recently. But an Israeli attack on the Palestinians at the same time could have even more serious consequences for the United States, especially if the U.S. were seen to be supporting such Israeli action, according to administration sources.