The Yugoslavs have heard the hints -- but so far they haven't reacted to the prospect that President Carter would like to make an official visit here late next month.
Mr. Carter's absence from President Tito's funeral this week was widely criticized in Europe. Yugoslavs were privately dismayed, though leaders refrained from comment.
Washington sources, however, make it clear that Mr. Carter would be interested in "substantive discussions" with the Yugoslavs in June.
A Carter visit to Belgrade would follow his state visit to Italy, his visit with Pope John Paul II at the Vatican, and then the economic summit of Western leaders in Venice on June 22 and 23.
Ever since Mr. Carter moved into the White House, the Yugoslavs have assured him that he would be "welcome here at any time." It has been a matter of regret that he has not yet found time. Now he is in the last year of his term, and President Tito is no longer here to be his host.
The Yugoslav leader himself visited three American presidents: John Kennedy in 1963, Richard Nixon in 1971, and Mr. Carter in early 1978. Both Presidents Nixon and Ford were here.
Undoubtedly the new Yugoslav leaders would like to have Mr. Carter visit before his term ends. But they might prefer that he did not come so soon after they finally and fully took up the reins of office.
Nevertheless, they would understand that the approach of the US presidential election might make it extremely difficult for the President to get away later. So, if a visit is to be made, June could be an acceptable time.
During the Tito years, the Yugoslavs developed a sophisticated attitude toward the numerous world leaders who visited them. Their welcomes are cordial to those they like, less warm but still correct to others about whom they have political reservations.
Mr. Carter would certainly be welcomed into the first category. American officials here -- as irritated as Washington over the barrage of criticism arising from his decision to stay home this week -- seem to be taking comfort from the thought that his presence here on an individual visit and "not as one of an enormous crowd" could have a greater impact.
They have also taken great pains to point out that it was Vice-President Walter F. Mondale whose visit here in 1977 broke the ice in a lengthy cold spell in US-Yugoslav relations.
Since then, the bilateral relationship has been better and more stable than at any other time in the postwar period. This was affirmed during the Vice-President's hour-long talk May 7 with Lazar Kolisevski.
Mr. Kolisevski -- as the presiding member of the eight-member state presidency -- is, in effect, President Tito's constitutional successor, but his one-year term expires shortly.
(He has wrongly been referred to as "seccond president of Yugoslavia." But the title "president of Yugoslavia" is reserved for Tito himself, and Mr. Kolisevski -- and those who take their yearly terms after him -- is "president of the state presidency.")
American officials here robustly refute the widespread reporting in the Western news media that the Yugoslavs are disappointed at Mr. Carter's absence. Ambassador Lawrence S. Eagleburger acknowledged that he originally recommended that the President attend.
"But," he said, "no Yugoslav has indicated to me the least unhappiness about the Vice-President being here instead. I don't think we have anything to apologize for, and I don't think the Yugoslavs feel we have anything to apologize for."
The Yugoslavs, of course, are too diplomatic to say anything out of place. Besides, Mr. Mondale is well regarded here.
But privately the Yugoslavs were somewhat disappointed, and the impression remains that Washington did not appreciate the symbolism of the moment as well as others -- especially the Russians.
Soviet President Brezhnev was among 19 presidents, three monarchs, 12 prime ministers, and a host of lesser luminaries who journeyed to Yugoslavia to pay tribute to Tito.
At least a million Yugoslavs, standing in long lines for four hours and more through the day and night, filed past his casket at the lying-in-state in the parliament building.
Almost as many watched in person Thursday in reverent silence, and the rest of the nation could follow on television, as the gun carriage bore it on the three-mile final journey to his resting place in the garden of his home in the leafy suburb of Dedinje overlooking this city.