The disclosure by the officials, who spoke on the condition of anonymity, comes as Defense Secretary Jim Mattis and Chairman of the Joint Chiefs of Staff Marine General Joseph Dunford hold closed door briefings with members of Congress about President Donald Trump's regional strategy.
The Pentagon said it would not comment on additional troop numbers until Mattis makes an announcement.
If confirmed, it would bring the total number of U.S. troops in Afghanistan to about 14,500.
After a monthslong review of his Afghanistan policy, Trump committed the United States last week to an open-ended conflict in the country and promised a stepped-up campaign against Taliban insurgents.
Last week Mattis said he had signed orders to send additional troops to Afghanistan but did not specify the size of the force, saying he first needed to brief Congress.
U.S. officials have for months told Reuters that Trump had given Mattis the authority to send about 4,000 additional troops to Afghanistan.
The U.S. presence in Afghanistan peaked at more than 100,000 troops in 2011, when Washington was under domestic political pressure to draw down the costly operation.
Some U.S. officials have told Reuters they questioned the benefit of sending more troops to Afghanistan because any politically palatable number would not be enough to turn the tide, much less create stability and security.
To date, more than 2,300 Americans have been killed and over 17,000 wounded in Afghanistan.
(Reporting by Idrees Ali and Phil Stewart; Editing by Bill Trott)
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