The right-hander, who has been out since straining his left hip abductor on June 30, will throw a bit over the weekend before Cooper decides his next start.
Brian Moehler is scheduled to start against the Cubs on Friday, followed by Wandy Rodriguez and Brandon Backe.
"We've got a spot on Monday," Cooper said. "Possibly [Runelvys] Hernandez will take that one, and we'll see how Roy is for Tuesday. If [Oswalt is] OK this weekend, then he'll take Tuesday."
Oswalt attempted to pitch against the Nationals on July 11, but he only threw 17 pitches in the first inning before coming out of the game.
Krysten Oliphant is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.