WASHINGTON (CNN) -- President Bush is likely to send anywhere from 20,000 to 40,000 additional troops to Iraq as part of his yet-to-be-announced new Iraq strategy, sources with knowledge of his deliberations told CNN Wednesday.

Bush is expected to address the nation on the new strategy early next week, sources have said.

The president has not yet signed off on any changes, including a possible increase of U.S. troops, according to the sources. But he is "driving toward a conclusion" and a plan is "taking shape" and "getting more detailed" as the president puts "on the finer points," they said.

National Security Council spokesman Gordon Johndroe denied a report Tuesday that Bush was ready to sign off on increasing troop strength in Iraq by 20,000, saying, "The president has not made any decisions."

Asked about the possible troop increase Wednesday, White House spokesman Tony Snow said Bush is "moving toward what he thinks is going to be the appropriate complex of policies to get that done."

"When the president announces the way forward, he will provide answers to a lot of questions that I'm not going to," Snow said.