The FBI is investigating, at the Justice Department's request, an allegation that secret South African funds were channeled into president Carter's 1976 primary campaign in New York state, it was learned yesterday.

Sources familiar with the matter said that so far, no support for the allegation, published in the South African newspaper Cape Times, had been found.

As a result, these sources said they believe the charge is not likely to survive the "preliminary investigation" that Attorney General Griffin B. Bell is required to conduct, under the ethics in Government Act of 1978, on any allegation involving the president.

The act provides that the attorney general must conduct a preliminary inquiry of up to 90 days into such charges, and that he must apply to a special court here for appointment of a special prosecutor if further investigation or prosecution is warranted. However, if he finds the matter so unsubtantiated that no further investigation is warranted, Bell is required only to notify the special court in a secret memorandum.

According to the newspaper article about $20,000 of a multimillion-dollar, secret South African Government fund went to Carter primary effort in New York at a time when Carter and other Democratic candidates were strapped for money.

Late last month, Assistant Attorney General Philip B. Heymann asked the FBI to investigate the allegation.