The expected increase would include at least three Army brigades and a single, larger Marine Corps contingent, officials said.
Both Democrats and Republicans in Congress has been miffed that the administration blocked McChrystal from testifying during what many Republicans considered an inordinately long decision-making period. His testimony has not been scheduled, but would probably come late next week or early in the week after.
The administration figures will have a tough sell among some congressional Democrats, including Senate Armed Services Committee Chairman Carl Levin, D-Mich., who has questioned the value of adding forces and pointed to the war's rising cost.
The Afghan war bill hit $43 billion annually this summer, with the addition of 21,000 forces Obama has already added to the fight this year. The White House has given Congress this rough yardstick for future troop increases: Approximately $1 billion a year for each 1,000 troops atop the current record figure of 68,000.
NATO and other allies collectively have about 45,000 troops in Afghanistan.
If the full expansion that US military planners anticipate does happen, it would take up to two years to get all the additional US forces into the landlocked country.
The United States is quietly pressing NATO and other allies to increase forces as well, with a goal of between 5,000 and 7,000 additional non-US troops. European and other diplomats have said that number is probably optimistic.
Obama's expected address is timed in part to come before a NATO foreign ministers meeting, taking place in Brussels, Belgium, at the end of next week.