Houston dislocated his right elbow two weeks ago against San Diego and missed Sunday's 35-28 loss to Denver, a game in which the Chiefs failed to sack quarterback Peyton Manning.
"We'll just see how he does," Reid said Monday. "I don't know if (playing Sunday) is real or not, but that's his mindset. We'll have to see how he does. He's in a day-to-day situation. He's made some strides but I think that'd be quite a feat if he were able to make it."
Left tackle Branden Albert hyperextended his left knee against the Broncos, while tight end Anthony Fasano sustained a concussion. Reid did not say with any certainty whether either of them will be available against the Redskins.
The Chiefs were forced to use Eric Fisher, their No. 1 overall draft pick, when Albert left the game. Fisher had been dealing with a shoulder injury that caused him to miss the Chargers game, and he started Sunday's game on the bench while Donald Stephenson got the nod at right tackle.
Reid said the decision to start Stephenson was not only because of Fisher's lingering injury, but also because Stephenson had performed well the previous week.
Fasano, who also tweaked his knee in the game, left with a concussion after his head slammed into the turf while he was attempting to catch a pass from Alex Smith in the second half. Fasano appeared woozy as he walked to the sideline and did not return, and Reid said that he was undergoing the typical concussion protocol on Monday morning.
"I've got to see how he is here over the next couple days. You see all different kinds of these things," Reid said. "I'm not here to rate him. I'm not a doctor. But just going off the symptoms he presented to us, he was feeling good today, so we'll see."
The Chiefs have been thing at tight end, a position that figures prominently in Reid's offense, for most of the season. Tony Moeaki went down with a season-ending shoulder injury during training camp, and Fasano missed four games earlier this season with an ankle injury.
Sean McGrath, who was claimed off waivers from Seattle, has proven to be a useful backup, but the Chiefs don't have much after that. Reid said he would huddle with general manager John Dorsey to discuss options in the event that Fasano cannot play against Washington.
He did say that a pair of practice squad tight could be promoted.
One of them, Demetrius Harris, was an undrafted free agent who played basketball at UW-Milwaukee but hadn't played football since high school. The other tight end, Dominique Jones, spent time with Indianapolis last season after playing collegiately at Division II Shepherd.
"That's an option," Reid said, "either one."