President Barack Obama is seeking to keep 9,800 US troops in Afghanistan after the US ends its combat mission in the country at the end of this year.
The US plan would reduce its current force of 32,000 by the end of 2014, halve that next year and remove nearly all troops by the end of 2016.
The remaining US military presence would train Afghan forces and support counter-terrorism operations.
But the plan depends on the Afghans signing a joint security agreement.
While current Afghan President Hamid Karzai has refused to sign such an agreement, the Obama administration appears to be confident either of the two candidates seeking to replace him would do so.
The president spoke to Mr Karzai by telephone to update him on the US plans, a White House official said.
Mr Obama's intended troop numbers are largely in line with what military commanders have been asking for and means he will leave office with the longest war in American history over.
He is to make a statement on his plans in a White House address at 14:45 local time (18:45 GMT).
The news will not affect the timetable for UK soldiers coming home, and all British troops are due to leave by the end of this year, the BBC has learnt.
At the weekend, President Obama paid a surprise visit to US troops in Afghanistan and on Monday at a Memorial Day ceremony he paid tribute to the more than 2,000 soldiers who have lost their lives in the country's longest w.