President Reagan yesterday denied a Washington Post report that some presidential advisers are urging that presidential counselor Edwin Meese III depart from the White House staff, possibly to become attorney general.

"The matter is made up entirely out of whole cloth. For those who don't understand, that means it's absolutely untrue," Reagan said, according to deputy White House press secretary Larry Speakes.

"There is no foundation and no basis for this," the president said.

Later, as Reagan walked to his helicopter to fly to Camp David for the weekend, he was asked about the story by reporters. "That is an entire invention that has never been heard of and there is not one shred of truth in it," Reagan replied.

At the daily White House news briefing, Speakes said: "I note that the only quotes in the story attributed to people by name are strong denials." The story depended on quotes of unnamed people to support its points.

In a separate development during the briefing, Speakes advanced--and then rapidly retreated from--the theory that the current recession began not in Reagan's presidency, but in the term of former president Jimmy Carter.

"I noticed this morning that the National Bureau of Economic Research . . . declared it began in July of '80," Speakes said. When a reporter asked whether Speakes was calling it the Carter recession, Speakes just smiled--happily.

A few minutes later, Jim Burnham, deputy to the chairman of the president's Council of Economic Advisers, hurried into the press room and handed Speakes a note. To the spokesman's chagrin, it said the recession started in July, 1981. Speakes blushed. "I thought you told me July '80," Speakes said as Burnham beat a retreat.