Smith told ESPN's Josina Anderson that the Texans decided to put Foster on the physically unable to perform list to begin training camp to alleviate any concerns that the right calf strain would linger.
"We want to make sure that he is totally 100 percent ready. So he's very close," Smith said. "We are just making sure that he is ready to go when we let him loose. We are being cautious and taking that slowly, but I have no worries that that is going to be something that he is going to have to deal with."
Texans coach Gary Kubiak told ESPN on Monday that Foster might be activated as soon as the middle of this week.
Foster rushed for 1,424 yards and 15 touchdowns last year for his third straight 1,200-yard season. He said Saturday that he feels good and that he expects to be activated from the PUP list soon.
Smith said Foster's focus coming into this season portends great things for him in 2013.
"He had his most productive year coming off of an offseason where he was just totally dedicated and focused. I saw the same dedication and focus this past offseason," Smith said. "So, if the last one was any indication, he's going to have a great year 'cause he worked and he was diligent in what he was doing this offseason. So he's committed to having an excellent season."
Foster's 351 carries led the NFL last season, but Smith said he isn't concerned that the running back has had too heavy of a workload.
"As it relates to the number of carries, you add the touches and receptions and it's up there, but I don't think that he has been negatively impacted by anything that he's done from a carries standpoint. I think Arian is one of those guys that likes the ball. He likes the ball in his hand. He likes the rhythm of the game," Smith said, also crediting backup Ben Tate for giving the Texans a potent "one-two combination."
Foster spent the offseason using a different training regimen in an attempt to try to "reinvent" himself. He said that the injury was what prompted the change but that it ended up being beneficial beyond that because he thinks doing the same workouts too much could cause a plateau in performance.
ESPN's Josina Anderson contributed to this report. Information from The Associated Press also was used.