"Military officials have declined to specify the timing of the departure, partly for operational security reasons and partly because many details are still quite fluid, and officials recognize that Mr. Trump could change his mind at any moment and speed up the departure".
Trump made a surprise visit to troops in Iraq last week.
Some critics also have expressed fear of a rapid withdrawal of US troops.
US-backed Kurdish militia has begun to withdraw from Manbij in northern Syria, inviting the Syrian army to move in as Turkey masses troops on the border.
The White House is considering the request and is inclined to agree, the official said.
He said Trump reassured him that the United States' Kurdish allies would be protected.
The Syrian regime said Wednesday hundreds of Kurdish fighters had withdrawn from Manbij near the border with Turkey, days after the Kurds appealed to Damascus for support against a threatened Turkish offensive.
Trump did not specify which generals he was referring to but his outgoing defense secretary, Marine Corps General James Mattis, resigned following the withdrawal announcement, issuing a barbed resignation letter in the process. Turkey considers the US-backed Kurdish People's Protection Units (YPG), which now controls almost 30 percent of Syria, a terrorist group linked to fighting within its own borders.
On Monday, the Republican president said the United States was "slowly sending" troops home - a markedly different tone than he used in his initial announcement of a withdrawal on December 19. The counter ISIS campaign continues, our efforts to counter Iranian aggression continues, and our commitment to Middle East stability and protection of Israel.
Roger Federer beats Cameron Norrie at Hopman Cup
It was an error-strewn start for Williams, who struggled to land her first serve and was broken in the third game. This year's Hopman Cup , the 30th edition of the tournament, is ongoing from December 29 to January 5.
Trump fought back against the criticism.
"I didn't like the fact that they [YPG] are selling the small oil that they have to Iran", Trump said during a Cabinet meeting at the White House in front of reporters.
"The results are FAR BETTER than I ever said they were going to be! We will continue the same way as before this decision was made", Pompeo said. We have other bases in the general area.
Though much reduced, and forced into hiding, it is still believed to comprise thousands of guerrillas. US-backed forces seized the jihadists' self-declared capital Raqa on Oct 17, 2017.
"Iran is pulling people out of Syria. They're going to Russian Federation, who hates ISIS more than we do", he said, using a different acronym for IS.
The view is popular with many Americans, but critics, including some of Washington's closest allies, say the United States can not abandon its traditional leadership role.
Netanyahu added, "We have a lot to discuss".
Trump's comments come a day after Republican Sen. Lindsey Graham (R, South Carolina) explained on Sunday.
After two hours, he emerged, saying Trump "understands the need to finish the job".