Just as Gerald Ford's hopes of making a late-starting bid for the presidency were dying for lack of support last month. Henry Kissinger held a private telephone conversation with William J. Casey, Ronald Reagan's campaign director.

The purpose of the March 14 conversation was clear: The former secretary of state wanted to open a door into the Reagan camp.

He knew Casey from the early days of the Nixon administration. A New York lawyer, Casey had been chairman of the Securities and Exchange Commission; Kissinger was Nixon's chief foreign policy adviser.

According the various Reagan sources, Kissinger told Casey that he considered Reagan properly qualified to be president; he said he had no personal animosity toward the former California governor; he promised that he wouldn't say anything to make it more difficult for Reagan to become president.

The intriguing thing about the conversation is that Kissinger has spent much of the previous two weeks trying toline up support for Ford. In fact, he had endorsed Ford, who in turn told reporters that he would name Kissinger as his secretary of state.

Kissinger's call to Casey was simply the latest in a series of low-key, but obvious, attempts by the former secretary of state to curry favor among Republican presidential contenders -- particularly those who appeared to be potential winners:

When John Connally's star was rising on the GOP horizon, Kissinger spoke at a Connaly fund-raiser and personally reviewed the major foreign policy address of Connally's ill-fated campaign.

when Sen. Howard Baker was enmeshed in controversy over SALT II and looked like a contender, Kissinger talked frequently with the Tennessee Republican. Later, he spoke at a Baker fund-raising affair.

When George Bush's stock soared after he won the Iowa precinct caucuses, Kissinger associates approached Bush's campaign staff offering assistance, according to Bush spokesmen.

But, with the contest for the GOP nomination moving into its final stages, Kissinger remains without a political patron: an adviser with no one to advise.

Each of the three remaining Republican contenders -- Reagan, Bush and Rep. John B. Anderson -- is on record as being opposed to having Kissinger serve as secretary of state. And each has gone out of his way to avoid any direct contact with Kissinger.

"I am sure Dr. Kissinger has a bright future ahead of him, but that future would not include public service in an Anderson presidency," Anderson declared during one debate.

Kissinger nonetheless appears ready and available.

"Many people have asked me if I would want to go through it all again," he said in a speech to editors last Thursday, referring to his days as secretary of state. "The problem is nobody has really asked me to."

"I'm not totally discouraged," he said at another point. "There's still some hope."

There is disagreement on when and why Kissinger began his latest courtship of the Reagan camp. He said in an interview that he placed a call to Casey on March 13, two days before Ford -- after several weeks of testing the political waters -- announced that he would not be a candidate for president.

Casey wasn't in and didn't return his call until the following day, Kissinger said. "My purpose was to try to keep personalities out of the debate between the two men [Ford and Reagan]."

Other sources claim that Kissinger didn't make the call until after Ford told him he wouldn't run. Kissinger denied this and insisted, "I've had no dealings" with anyone on the Reagan campaign since Ford dropped out.

The timing of the call is less crucial than the fact that it was made, and that it was interpreted in the Reagan camp as extending a peace pipe.

Kissinger never has been a favorite among Reagan's supporters. Earlier this year, the candidate told a Chicago press conference that, if elected, he wouldn't name Kissinger his secretary of state.

To Reagan's followers, the marks against Kissinger are clear.He is widely suspect among many conservatives for his support of detente and for his role in normalizing relations with China. And, Richard V. Allen, Reagan's top foeign policy adviser, had left a job on the National Security Council during the Nixon presidency because of his unhappiness with the way Kissinger operated.

Allen, regarded as the right-winger in residence on the council, had resented the way Kissinger controlled information and access to Nixon.

But far more damaging to Kissinger's prospects of finding a major role in a Reagan presidency was his effort to encourage Ford to enter the GOP race. Reagans advisers always have held a special fear of a Ford candidacy. They have felt that their candidate easily can fend off challenges from the George Bushes and John Andersons of the world, but that one by former president Ford could be another matter.

These circumstances made Kissinger's speech before the American Society of Newspapers Editors last week a fascinating event. The address was a masterful piece of oratory, combining a biting denuncuation of Carter's foreign policy with historical perspective and some rays of hope.

It was, New York Times columnist James Reston wrote, the "only really presidential speech" the editors heard during a week that included appearances by Carter, Sen. Edward Kennedy, Reagan, Bush and Anderson.

Kissinger, others said, had gone public with his campaign to become the next secretary of state. He sounded like an elder statesman in exile, somberly viewing a troubled homeland.

Much of his address appeared to be directed at a man who was not present -- Reagan.

Diplomatic insiders noticed several new twists in Kissinger's remarks. One was a reference to fears expressed by some Reagan defense advisers that U.S. defense policy was based on an over-reliance on nuclear weapons.

Later that day, Kissinger was asked at a Baltimore press conference who he would vote for in November if the choice were between Reagan and Carter.

Reagan, he replied.