Penny, who was selected 27th overall by the Seahawks in the 2018 NFL Draft, sustained a broken finger in practice last week. Multiple media outlets reported that he would be sidelined for three to four weeks.
"He's running around already," Carroll told reporters on Tuesday. "He's back in terms of conditioning and moving and all that kind of stuff. We're very fortunate he's going to be able to get back right away. It's just a matter of making sure that it's secure and quiet it down. He'll run all week long and he could be ready for next week, for sure be ready for the opener."
Penny had been competing with Chris Carson for the starting running back job with the Seahawks, who had just one rushing touchdown outside of quarterback Russell Wilson. Wilson, in fact, led Seattle in rushing last season with 586 yards -- 346 more than Mike Davis.
Carson held the top spot in the team's most recent depth chart, with Penny ahead of Davis and C.J. Prosise, among others. Penny rushed for just 16 yards despite a team-high eight carries in the Seahawks' preseason opener against the Indianapolis Colts.
"He's a fantastic competitor in that he's applied himself so much to get his pass protection stuff right," Carroll said. "He knew what he needed to do in terms of scheme, as well as the physical side of it. He worked hard on it on the offseason so when he showed up, he wouldn't be behind. Those are great signals that he gets it, and he knows what's important.
"When he's been out here and dialed in, he's always asking questions, he's always trying to figure it out, he always wants to do things better, he wants more turns. He wants to get more reps (and) he doesn't want to come out of the game. He's shown nothing but great stuff. We're really pleased and fired up about it, we've seen him run through traffic and the things that he can do."
Penny led the nation with 2,248 rushing yards to go along with 23 touchdowns last season at San Diego State. He also had 19 receptions for two more scores.
The 5-foot-11, 220-pound Penny averaged 7.8 yards per carry last season and 7.5 yards in 2016, when he rumbled for 1,018 yards rushing and 11 touchdowns.
Penny also was a weapon in the return game for the Aztecs, bringing back seven kicks for touchdowns in his career. Penny averaged 30.2 yards per return for his career.