South African Foreign Minister Roelof F. (Pik) Botha said yesterday that the United States "has a real chance of achieving an internationally accepted solution" to the issue of independence for Namibia, but neither he nor senior U.S. officials offered any hope that an agreement is near.

In a continuation of the Reagan administration's policy of "constructive engagement" with South Africa, Botha met yesterday with Secretary of State George P. Shultz, Undersecretary for Political Affairs Lawrence Eagleburger and the State Department's chief Africa-policy strategist, Assistant Secretary Chester Crocker.

On a visit in May, 1981, at the outset of the new administration's approach toward South Africa, Botha met with President Reagan as well as with then-Secretary of State Alexander M. Haig Jr. Both Reagan and Vice President Bush, who just completed a tour of several black African countries, were out of town yesterday.

U.S. officials said the meetings primarily were intended as a get-acquainted session for Botha and Shultz and not for negotiations, but South African diplomats said talks yesterday and on Wednesday between Crocker and Botha centered heavily on the Namibia issue.

Expressions of optimism over Namibia, common from U.S. officials this past summer, have begun to wane in recent months. Namibian independence has been publicly linked by Washington to withdrawal of Cuban troops from neighboring Angola and this "linkage" has been condemned by many African states.

A U.S. official said yesterday Americans should "not be deceived by the rhetoric" of African leaders on the Cuban issue, arguing that "of necessity many leaders have to state their rejection publicly, but practically all . . . support our effort for a negotiated settlement."

The official, whose remarks were on a non-attributable basis, warned that "there is the potential for southern Africa to slide into real danger." He said Botha and Shultz focused on the "security situation" in all of southern Africa, an apparent reference to reported South African destabilization efforts in Mozambique, Zimbabwe and Zambia.

South African troops have been operating in southern Angola for some time in connection with the guerrilla war over Namibia.

Botha said after his meetings with Shultz, which lasted some three hours, including lunch, that in the Namibia negotiations "the major problem is the lack of trust by the Angolan government." It was a sentiment endorsed by the U.S. official, who said, however, that the lack of trust exists on both the Angolan and South African sides.

Asked about reported suggestions that a multinational force might be formed to take the place of Cuban troops in Angola, Botha said the idea has not been formally proposed but that South Africa "will not be able to tolerate foreign forces" in the region.

The U.S. official, admitting that the idea had been one of many informally discussed, said that while Washington had not proposed such a force, neither had it been ruled out.