Lawyers for the indicted owners of New York's Studio 54 discotheque have a tape recording in which a reputed drug dealer makes a detailed reminiscence of watching White House Chief of Staff Hamilton Jordan use cocaine last year, according to a source close to the case.

On the other hand, other sources familiar with the investigation said that the reputed dealer, John (Johnny C) Conaghan, told the FBI earlier this week that he could not corroborate the allegation of Jordan's drug use.

The conflicting stories of Conaghan's recollections are the latest twist in a tale that has become a political sore spot for the Carter administration and an increasingly unsolvable dilemma for new Attorney General Benjamin R. Civiletti.

Civiletti last week ordered the FBI to start a preliminary investigation of the alleged cocaine use after the disco's owners, Ian Schrager and Steve Rubell, made the charge during pleabargaining talks with prosecutors in New York.

The men were indicted in June on tax charges of skimming $2.5 million in cash from their club's operation. Though a first offense for possession of cocaine is not usually prosecuted, the allegation against Jordan automatically triggered the special-prosecutor provisions of the new Ethics in Government Act.

Mitchell Rogovin, Schrager's attorney, said last night that he has "tangible evidence in a neutral setting in which 'Johnny C' corroborates the use by Jordan of cocaine."

He said he was not "surprised that 'Johnny C' denied the facts in light of the potential criminality attached to it. It is my understanding that during such a preliminary investigation no immunity can be offered to a witness."

Rogovin said he would turn the evidence over only to a special prosecutor.

A Justice Department official familiar with the case said he also was not surprised that Conaghan denied the story by the Studio 54 owners. "What do you want him to tell a couple of FBI agents, 'Yeah, I gave Ham Jordan some coke?"

A source close to the defendants said that during a conversation with Rubell within the last month, Conaghan described the June 1978 incident in which Jordan allegedly used cocaine in the basement of Studio 54.

The discussion of the occasion took about five minutes, and was taped without Conaghan's knowledge, the source said.

During the conversation, Conaghan recalled how Jordan sniffed the cocaine from a spoon and then snorted some in each nostril, it is said. Conaghan also said he thought Jordan had used the drug before, though not regularly, the source said.

Jordan has denied the incident, and the White House has said the accusers were making inaccurate charges in an attempt to get prosecutors to settle the tax-evasion case.

One official close to the case said it is likely that Civiletti will have to ask a special court to appoint a special prosecutor. Under the terms of the new law, Civiletti must do that after 90 days unless he can positively conclude that the charge is unsubstantiated.

Attorneys for the defendants have said they will let the FBI question their clients about the Jordan charge only as part of a settlement of the tax case.

Rogovin yesterday said he told prosecutors from the beginning -- even before naming Jordan -- that he didn't believe the alleged cocaine case was prosecutable. "It's a question about the propriety, the conduct of a high government official," he said.

He said drug use could be used to blackmail an official."From my experience with the Central Intelligence Agency, I'm confident that if they had such information on the number two man in a foreign government they wouldn't hesitate to use it," he said. Rogovin was a lawyer for the CIA.