He was effectively conceding another legal reverse in the fight to clear his name over allegations of witness-tampering.
The President has tried to claim that his conversations with Bruce Lindsey and Sidney Blumenthal were covered by executive privilege. But he has been outmanoeuvred by Kenneth Starr, the independent counsel.
Mr Starr is investigating claims that Mr Clinton had an affair with former White House intern Ms Lewinsky, 24, and that he and his advisors persuaded her to lie about it, thus committing perjury.
A United States judge ruled that the two aides were not covered by executive privilege, saying the arguments were not strong enough to overcome the grand jury's interest in obtaining evidence of possible crimes, but leaving Mr Clinton the chance of appealing to a higher court.
Mr Starr had asked the US Supreme Court to make an urgent ruling, thus bypassing the appeals process.
Reports yesterday said that the President was expected to drop the appeal, clearing the way for the investigation to continue and the aides to testify.
A Clinton appeal would have raised parallels with former president Richard Nixon, who also fought to claim executive privilege over the White House tapes.
Instead, the President will claim that his conversations with Mr Lindsey were covered by attorney-client privilege, a less controversial claim.