John W. Hinckley Jr. reportedly wrote that he was in conspiracy with others when he shot President Reagan, and also described in writing purportedly fictional co-conspirators, apparently thinking that he could trade the "information" to make a favorable deal for himself.

A Justice Department spokesman said last night that a continuing FBI investigation into the March 30 shooting "has developed no reliable evidence of a conspiracy." Both the Justice Department and the U.S. Attorney's office in Washington refused to comment on a report by Gary Reals of WDVM-TV (Channel 9) that Hinckley allegedly concocted the conspiracy scheme. The report also said that prison officials intercepted letters from Hinckley to "co-conspirators."

According to that report, Hinckley's plan was discovered last July when guards at the federal correctional institution at Butner, N.C., found writings about the alleged conspiracy among Hinckley's papers during a routine search of his cell.

Those documents, which have been the subject of hearings in U.S. District Court in Washington for the past two days, were seized by prison authorities and turned over to the FBI. Copies of the documents have been kept under seal at the court here. During the hearings, witnesses had been ordered not to discuss the contents of the writings during their public testimony.

Hinckley's lawyers contend that the search that uncovered the alleged conspiracy documents was illegal because Hinckley had a right to expect that his personal papers would be kept private. They want Judge Barrington D. Parker to prohibit the government from using the documents at Hinckley's trial. The government contends, however, that Hinckley was informed that his cell would be searched.

After it was learned by the court that the contents of the documents had been leaked to a reporter, Judge Parker delayed the hearings for more than an hour yesterday while he met with prosecution and defense lawyers in his chambers. Following the delay, the proceedings were abruptly adjourned for the day and will be resumed Monday.

Hinckley, 26, will contend at his trial, now scheduled for Nov. 30, that he should not be held criminally responsible for his acts because he was insane at the time he shot Reagan, his press secretary, a U.S. Secret Service agent and a D.C. police officer.

A federal court order prohibits lawyers in the case and law enforcement officials from public discussion of the Hinckley case. The Justice Department was recently ordered to investigate a leak to United Press International about telephone conversations between Hinckley and actress Jodie Foster prior to the Reagan shootings. Law enforcement sources, who confiscated an unmailed letter for Foster from Hinckley on the day of the shootings, believe that Hinckley's assault on the president was an attempt to impress Foster.

U.S. Attorney Charles F.C. Ruff said last night that no steps had been taken to investigate the disclosure of information about Hinckley's writings to the Washington television reporter.