Smith says he "looked pretty good" on Monday, but he wouldn't put a timetable on Forte's return.
"As far as when, I'll just say we're still evaluating him," Smith said. "He looked pretty good this morning, but it is an MCL. He didn't finish the game. So there is concern."
Forte was injured in the first quarter of Sunday's 10-3 loss to Kansas City and left the game. An MRI on Monday confirmed the initial diagnosis, and there is no ligament damage to the ACL, a league source told ESPN NFL Insider Adam Schefter.
Injuries such as these typically sideline players two to six weeks. There are four games left in the season.
"Going into the fourth quarter of the season, we should be in pretty good shape," Smith said. "Can't tell you exactly when (he'll be back), whether it's this week, next week or whatever. But hopefully we'll get him back soon."
Forte has been lobbying for a new contract, but Smith did not think that his status would affect his pace of rehab.
"No, I don't think that will come into play," Smith said. "I think all players in the NFL will try to do whatever they can to help their team win. We will not play a player that's injured. Once you have a healthy player, I think they're all ready to go. And I know that's the case with Matt Forte. He can't wait to get back out on the football field to help his team win."
Chicago already was missing quarterback Jay Cutler, who is out indefinitely with a broken right thumb.
Smith says the Bears won't bring in a veteran quarterback even though Caleb Hanie is struggling, squashing speculation that they'll sign Donovan McNabb. He also dismissed a report that offensive coordinator Mike Martz will be gone after the season.
Information from ESPNChicago.com's Michael C. Wright and The Associated Press was used in this report.