The FBI is seeking the Justice Department's permission to give lie detector tests to about a dozen people to resolve inconsistencies that have developed during the investigation into how Ronald Reagan's 1980 presidential campaign obtained documents from the Carter White House, government sources say.

Included on the list of those to whom the FBI wants to give polygraph tests are CIA Director William J. Casey and White House chief of staff James A. Baker III. Baker has said he received Carter briefing papers for the 1980 presidential debate from Casey, while Casey has said he does not recall seeing the papers or handing them to anyone.

Justice Department spokesman John K. Russell yesterday said there would be no comment on any methods the FBI might want to use in its six-week-old investigation.

But official sources yesterday said the FBI was interested particularly in Casey, who directed Reagan's 1980 campaign and has denied that it included an intelligence operation seeking information and documents from inside the Carter campaign.

Justice Department investigators, however, have discovered a memo in the Reagan campaign files from aide Max Hugel to Casey that conveyed what one investigator said was "a strong, unavoidable inference" that such an operation was receiving information from someone working for Carter. The Hugel memo did not name the person, the sources say.

"Anyone reading the memo would conclude that there was an agent--someone working for Carter but supplying information to the Reagan campaign," according to another official who said that was his interpretation after reading the memo.

The memo does not conclusively prove the existence of such an operation, however, the officials said. They added that even if such an operation existed it is not clear whether any law was violated.

Officials said they have not found anything illegal in the transfer of non-classified documents such as Carter debate briefing papers that wound up in the files of Reagan campaign officials. Investigators also are studying the question of classified documents, but officials said they do not have evidence that any were improperly obtained by Reagan campaign aides.

It could not be learned yesterday whether Hugel is among the 12 persons the FBI wants to re-interview with a lie detector. He could not be reached for comment yesterday, but he had issued a categorical denial to a Time magazine report suggesting that he was involved in a Reagan campaign intelligence operation.

After Reagan's election, Hugel was named by Casey to run the CIA's covert operations. He resigned in 1981 after questions were raised about his previous stock and business dealings.

Casey and Baker already have been interviewed formally by the FBI, but investigators want to re-interview them and request polygraph tests, according to government sources. FBI policy in such investigations leaves it up to the individual whether he will take a lie detector test.

A CIA spokesman yesterday said Casey was unavailable for comment. But he emphasized that Casey would continue to cooperate with the separate investigations being conducted by the FBI and a House subcommittee chaired by Rep. Donald J. Albosta (D-Mich.).

Baker was out of town yesterday. But White House officials previously have said Baker is anxious to have the investigations completed. One official said Baker probably would be willing to do anything--"swim the English Channel, if necessary"--to clear his name.

Officials said President Reagan also was interviewed by FBI agents recently and cooperated fully. Officials said he repeated his public statements that he had no knowledge that his 1980 campaign obtained any documents or information from the Carter campaign or White House.

The FBI does not intend to re-interview the president or seek a polygraph test from him, officials said. Reagan has publicly and privately instructed all members of his administration to cooperate fully with the FBI.

The chief dispute the FBI seeks to resolve with lie detector tests is between Casey and Baker. In a June 22 letter to Albosta, Baker said, "I do remember briefly seeing a large loose-leaf bound book . . . that was thought to have been given to the Reagan camp by someone with the Carter campaign . . . . It is my best recollection that I was given the book by William Casey, with the suggestion that it might be of use . . . ."

In his letter to Albosta's subcommittee, Casey said, "I have no recollection that I ever received, heard of or learned in any other way of a set of papers which laid out the Carter debate plan or the points which President Carter had planned to make . . . . I can assure you that the campaign management never contemplated, directed or authorized any effort to obtain information of this kind nor, to my knowledge, did the campaign ever use or have the kind of information . . . ."

In later press interviews Casey went further, telling The New York Times: "It would be totally uncharacteristic and quite incredible that I would hand anybody a book I knew to be from the Carter campaign and say this might be helpful to the debate . . . . I wouldn't tolerate it . . . . I wouldn't touch it with a 10-foot pole."

Both Baker and Casey reaffirmed their conflicting accounts in their initial interviews with the FBI, according to officials. One said Baker strongly asserted to investigators that Casey had given the material directly to him shortly before the Oct. 28, 1980, Reagan-Carter debate.

According to one official source, the CIA director told the FBI he had no recollection of Carter debate briefing papers but did not rule out the possibility that in the busy final days of the campaign something had passed through his office or across his desk.

Several of the officials involved in the Carter papers investigation expressed concern about giving a lie detector test to the current CIA director. It was not clear yesterday whether the Justice Department would permit it. Official sources said Casey was friendly and fully cooperative in the initial FBI interview.

Interviewing the CIA director is a particularly touchy matter for the FBI because the two agencies have not always had the best relations.