"I'm going to shoot for playing during this homestand at some point," Bour said.
The next couple of days will be telling as Bour increases his activities.
"[Thursday] was the first time I was able to run with minimal discomfort," Bour said. "We're just progressing as we can."
When cleared to play, Bour will likely play a couple of rehab games for Class A Advanced Jupiter.
"He kind of turned the corner the other day," Marlins manager Don Mattingly said. "He's able to do the agility of running without pain. If we're able to do that for two or three days, through the weekend, I would think early next week is something that is conceivable at this point."
With Bour out, Chris Johnson and Don Kelly have filled in at first base.
"It's tough to have a season where everyone is 100 percent," Bour said. "I think it is times like this when you see what a team has. Obviously, we have a lot of depth, and we've found a way to win games with guys being out."
Getting Bour back would provide another power threat to the lineup.
Bour is batting .268/.347/.526 with 15 home runs and 46 RBIs.
"I'm hitting at 100 percent, there are no problems there," Bour said. "Not feeling any pain there. It's just a matter of getting me to where I need to be defensively and running. The deceleration, when running, is something we need to build up strength. I've been here every day since pretty much I got hurt.
"I'm ahead of schedule. Hopefully, get the OK [soon] to go ahead and start a rehab assignment."
Joe Frisaro has covered the Marlins for MLB.com since 2002. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.