He went through a pregame routine that consisted of stretches and some light work in the batting cages prior to Sunday's series finale against the Brewers.
"[The soreness] is around the whole ankle, so it's not like a sprain. I think I just jammed it," Bourn said. "I can ride the bike and loosen it up. I'm going to take [batting practice] in the cage after chapel.
"I don't think it'll hurt to swing; I just think it'll hurt to run. I can put pressure on it and stuff like that."
Houston manager Cecil Cooper was positive when speaking of Bourn's condition, but said that the Astros would be cautious with him.
"It might take a couple of days," Cooper said. "He was walking gingerly today; the hope is he'll feel better tomorrow."
Bourn hurt the ankle on a play in the top of the sixth inning of Saturday night's 6-4 loss to the Brewers when he tried to break up a double play at second base. Bourn was 2-for-3 on the night before being replaced by Darin Erstad following the injury.
"When it just starts getting good, I have to sit down," Bourn said. "I was just trying to break up that double play, so we could get the run. But I got hurt, we didn't get the run and we got the loss."
The speedy outfielder knows that the injury could have been much worse and that his legs are a big part of his game.
Cooper is eager to get Bourn back because the outfielder has been very successful at the plate in recent weeks. He is hitting .400 since July 9, the highest average among Astros players during that span.
"He's been getting some hits," Cooper said. "He's been limiting his strikeouts, not hitting the ball in the air and those kinds of things. He certainly has been playing better, and hopefully, he's taking it to [mean] that if he plays well, he plays."
Dave Fultz is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.