Ortiz (2-0) missed the 2008 season after undergoing Tommy John elbow ligament replacement surgery, but he made the team this year as the No. 5 starter. He's made three starts so far and appeared in six games overall, sporting a 5.21 ERA in 19 innings.
Ortiz would start against Ted Lilly in Thursday's game.
"He threw a light 'pen [session] last night and should be ready to go on Thursday," Cooper said before Tuesday's game against the Nationals. "He was available yesterday. He's probably not available today."
Ortiz made his most recent start April 26 against the Brewers, picking up a win in the Astros' 3-2 victory. He gave up two runs on four hits in five innings. Ortiz has gone five innings in each of his past two starts after getting through 4 2/3 innings in his first start of the season.
The team's recent off-day and Roy Oswalt's rain-shortened start on Saturday have jumbled the starting rotation a bit, and Ortiz's turn was skipped last week. He did come in to pitch one-third of an inning in Sunday's 7-5 win over the Braves, throwing just 12 pitches.
Cooper had said before Monday's 9-4 loss to the Nationals that Ortiz would be available if needed, since the bullpen had thrown 12 innings in the past two games. But Cooper used three other pitches in that game after starter Brian Moehler went five frames.
Jeff Seidel is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.