When the White House buckles down to the difficult task of finding a new secretary of transportation later this week, look for an effort to find a high-powered, well-known figure who would enhance the Reagan Cabinet.

At least one White House official has come up with the extraordinary idea of turning to Chrysler President Lee A. Iacocca to take the place of Secretary Drew Lewis, who has resigned effective Feb. 1.

"Drew was a star," this official said. "It will take a star to fill his shoes."

Iacocca, who brought Chrysler back from the brink of fiscal disaster, is liked and respected by Reagan and has been a supporter of the president's economic program. He would also, as one official puts it, "add some pizazz to the Cabinet."

That accusation is unlikely to be leveled against others on the laundry list of prospective candidates. Among them are Deputy Transportation Secretary Darrell M. Trent, Federal Highway Administrator Raymond A. Barnhart, presidential assistant Elizabeth Hanford Dole, former representative Thomas B. Evans Jr. (R-Del.) and Los Angeles County Supervisor Pete Schabarum. If the choice is made from this list, the edge may go to Dole, whose assets include wide-ranging Washington experience and the added benefit of easy Senate confirmation.

But the betting at Palm Springs, where the president spent the final week of 1982, was that a celebrity of Iacocca's stature would be sought to bolster a Cabinet short on stars.

Whether the Chrysler executive would take the job, if it is offered, is not known.

Midway through the presidential holiday last week, members of the White House press corps were tempted to issue a missing person's bulletin for the president. Reagan was kept far away from press pools assigned to him as he was whisked from party to party. Reporters, infrequently not even within viewing distance of Reagan, were searched and scanned by metal detectors for no apparent reason.

But Reagan, who has become far more accessible in the last few weeks, took the edge off this concern by approaching one pool and answering questions about various issues. On New Year's Eve, he also dropped in at a party for the White House press.

Clad in golfing slacks and a red sweater, the president strolled around the room, shaking hands and chatting with reporters, one of whom asked whether the round of parties was getting to him. Reagan shook his head.

"It's not the parties, it's the meetings," he said.

The White House, incidentally, threw some business the way of an old Reagan buddy, cowboy Gene Autry, during the holiday trip.

The press was quartered at Autry's hotel in Palm Springs, a 15-minute drive from the Marriott Hotel in Palm Desert where Reagan's staff was sequestered.

This followed a recent pattern on Reagan trips, a policy apparently aimed at keeping reporters as far away as possible from the staff.

Reaganism of the Week: Launching into a speech about military preparedness aboard the battleship New Jersey in Long Beach Harbor last Tuesday, the president said he felt as if he were back on the set of "Hellcats of the Navy," his last made-for-cinema movie in 1957.

"I remember at the time I was in love with my leading lady," Reagan said. "She is Nancy, my wife, and I'm still in love with her, but I have to confess that today I find myself developing a great respect for the leading lady in these ceremonies.

"She's gray, she's had her face lifted, but she's still in the prime of life, a gallant lady: the New Jersey."

Reagan is back in town for the next two months, except for a trip one week from Tuesday to Dallas where he will make a farm speech. Today, he will receive a firsthand report on prospects in the new Congress when he meets with Republican congressional leaders, then hosts a bipartisan leadership dinner at the White House. Later this week, he is to meet with new members of the 98th Congress, most of them Democrats.

Early last week, a report gained currency on the West Coast that former president Richard M. Nixon would be invited to the New Year's Eve party at the Walter Annenberg estate where the Reagans were guests of honor. White House spokesman Larry Speakes called a briefing to douse the rumor. What Nixon really said, quipped The Washington Times' Jeremiah O'Leary, was: I am not a guest.