An article yesterday about U.S. Ambassador to the Vatican William A. Wilson incorrectly stated that the Pennzoil Co. has business dealings in Libya.

President Reagan has full confidence in William A. Wilson, his longtime friend and ambassador to the Vatican, the White House said yesterday, but did not know in advance of a Wilson mission to Libya that drew a rebuke from Secretary of State George P. Shultz.

Spokesman Larry Speakes, who was unusually guarded yesterday in discussing Wilson's activities, said, "There were no authorized missions . . . either at the ambassadorial level or any other level" to Libyan leader Muammar Qaddafi in January, the time when Wilson traveled to Tripoli. Reagan learned of Wilson's trip "after the fact," Speakes said.

Qaddafi, speaking to reporters Jan. 5 from a tractor in a barley field near Tripoli, disclosed that an American ambassador had contacted Libya "during the last few days" to suggest that the tension in U.S.-Libyan relations "should be defused and we should start with resuming commercial relations."

Under questioning, Qaddafi said he did not know the name of the U.S. envoy but added, "He's an ambassador -- maybe the American ambassador in the Vatican."

Qaddafi's comments were greeted with denials in Washington, where the policy guideline was to isolate the Libyan leader following the Dec. 27 terrorist attacks on the Rome and Vienna airports, rather than to negotiate or do commercial business with him.

In response to Qaddafi's remarks, White House spokesman Bill Hart said "we are not aware of any such contact." The same statement was made by State Department spokesman Dan Lawler, who added that "no such contact has been authorized."

Department officials said yesterday that Wilson's trip to Libya came to light days later and then only because his U.S. security guards reported that he had disappeared for a day without explanation shortly after the airport attacks.

Shultz subsequently discussed the matter in a private meeting with Wilson. The ambassador "admitted that he did it," a State Department official said, but insisted that his overtures to Qaddafi had been authorized by former national security affairs adviser William P. Clark.

Asked about this yesterday, Clark said "there was no authorization to Ambassador Wilson or anyone else to carry on unilateral communication with Qaddafi."

Wilson, who did not respond to an inquiry on the subject through his embassy at the Vatican yesterday, is a longtime friend of Reagan and a member of his informal "kitchen cabinet." Wilson found the ranch north of Santa Barbara where Reagan spends much of his leisure time. A millionaire California developer, Wilson has served as co-trustee of The Ronald Reagan Trust, which manages Reagan's financial affairs.

In an exception to normal U.S. diplomatic rules, Wilson was permitted, while ambassador to the Vatican, to continue serving on two corporate boards of directors, including the Pennzoil Corp., which has dealings in Libya. About a month ago, this exception was revoked and Wilson was ordered to resign from the corporate boards, a State Department official said.

Wilson has long been interested in improving relations with Qaddafi and has been communicating with Libya "over a period of time," said a source familiar with his thinking.

Echoing comments of columnist William Safire of The New York Times, which first reported Wilson's unauthorized trip, reporters asked Speakes to compare the gentle public treatment of Wilson with the firing of U.N. Ambassador Andrew Young in the Carter administration for an unauthorized meeting with the Palestine Liberation Organization. "A different man was president at the time," Speakes responded.