These officials said Stephen Hadley, the president's national security adviser, was meeting with key Republicans in hopes of sealing an agreement that could allow the legislation to clear Congress before lawmakers adjourn for elections.
President Bush's call for legislation has been deadlocked in an intraparty dispute, with Republican Sens. John McCain of Arizona, John Warner of Virginia and Lindsey Graham of South Carolina seeking a provision to make it clear that torture of suspects is barred.
Also at issue was whether suspects and their lawyers would be permitted to see any classified evidence in the cases against them.
Warner, McCain, Graham and Hadley met at mid-afternoon with Senate Majority Leader Bill Frist in the Capitol. CBS News correspondent Sharyl Attkisson reports they are working out language for the deal.
The session came a few hours after Frist phoned the lawmakers and strongly urged them to reach a compromise after more than a week of Republican discord.
White House spokeswoman Dana Perino said in an e-mail there was not yet an agreement, but added, "Good trajectory. Stand by for confirmation."
No details of the emerging compromise were immediately available.
Nor was it clear how Senate Democrats might react.
An accord would fulfill a Republican political and legislative imperative — pre-election party unity on an issue related to the war on terror, and possible enactment of one of Mr. Bush's top remaining priorities of the year.
The evident compromise came less than a week after Mr. Bush emphatically warned lawmakers at a news conference he would shut down the interrogation of terror suspects unless legislation was sent to his desk. "Time's running out," he said.
The White House shifted its tone from combative to compromising within 48 hours, though, and officials began talking of a need for an agreement that all sides would be comfortable with.
With November elections for control of Congress just weeks away, congressional Democrats are sitting out the negotiations, letting the handful of Republican senators battle the Bush administration.
Senate Minority Leader Harry Reid, D-Nev., said Wednesday that Democrats were "on the sidelines watching the catfights" among Republicans on terrorism legislation. He said they had little choice until the GOP settled on its position.
Whatever the outcome, the controversy has handed critics of the president's conduct of the war on terror election-year ammunition.
Mr. Bush's former secretary of state, Colin Powell, dismayed the administration when he sided with Warner, McCain and Graham. He said President Bush's plan, which would have formally changed the U.S. view of the Geneva Conventions on rules of warfare, would cause the world "to doubt the moral basis" of the fight against terror and "put our own troops at risk."
The handling of suspects is one of two administration priorities relating to the war on terror.
The other involves the president's request for legislation to explicitly allow wiretapping without a court warrant on international calls and e-mails between suspected terrorists in the United States and abroad. One official said Republicans had narrowed their differences with the White House over that issue, as well, and hoped for an agreement by day's end.
Republican leaders have said they intend to adjourn Congress by the end of the month to give lawmakers time to campaign for re-election.
The Supreme Court ruled in June that Mr. Bush's plan for trying terrorism suspects before military tribunals violated the Geneva Conventions and U.S. law.
The court, in a 5-3 ruling, found that Congress had not given President Bush the authority to create the special type of military trial and that the president did not provide a valid reason for the new system. The justices also said the proposed trials did not provide for minimum legal protections under international law.
About 450 terrorism suspects, most of them captured in Afghanistan and none of them in the U.S., are being held by military authorities at Guantanamo Bay, Cuba. Ten have been charged with crimes.