"We'll see what the doctors have to say, when they actually want him to go," he said.
An eight-time Pro Bowl selection, Harrison injured his left knee early last season, causing him to miss 11 games. He also had surgery on his right knee during the offseason to clean out old scar tissue, but he has appeared to be rounding back into form since reporting to training camp last week.
Dungy said nothing has happened in camp to hinder Harrison's return.
"It's more a doctor's schedule," Dungy said. "He's right on schedule in terms of practicing and running. And when we want the live work (in a game), whether it will be (preseason) week three or week four, we'll see."
Harrison is one of 12 Indianapolis players not expected to suit up for the Washington game, along with quarterback Peyton Manning (knee), linebacker Tyjuan Hagler (pectoral muscle), defensive end Dwight Freeney (foot), safety Bob Sanders (shoulder), offensive guard Ryan Lilja (knee), tight end Tom Santi (knee), safety Melvin Bullitt (thumb), receiver Charles Dillon (foot), defensive end Ben Ishola (foot), linebacker Gary Brackett (hip) and linebacker Clint Session (calf).
