Carroll said Browner continues to recover and was expected to run on Wednesday. If there are no setbacks, Browner is expected to go through practice Thursday.
Walter Thurmond started in Browner's place against the Panthers with Byron Maxwell also seeing significant time when the Seahawks added another defensive back.
"It looks like he has a real chance to make it back. We're going to do it right and not push it too soon, but tomorrow will be a big day for us to understand more," Carroll said.
Carroll also expects defensive end Cliff Avril to be able to play against the 49ers after he missed Sunday's season opener, also with a lingering hamstring injury. Avril said he was close to being able to go against the Panthers, but trainers felt it best to hold him out.
Avril was the Seahawks' biggest offseason signing in free agency in an attempt to bolster the pass rush. He was first slowed by a foot problem at the start of training camp before the hamstring injury popped up.
"It was kind of a battle between the trainers and myself actually," Avril said of last week. "It was pretty close, but hopefully I keep progressing and I'm able to put three good days together and be able to get out there this week."
Avril's return would be a major addition to a defensive line whose depth was a question going into the opener. Defensive tackles Tony McDaniel and Brandon Mebane were able to make it back from groin injuries to play against the Panthers, but getting Avril would be a boost heading into the highly anticipated matchup with San Francisco.
"I can't wait to get in front of the home crowd and hopefully be able to make a few big plays and show them, hopefully, what I can bring to the team," Avril said.
Seattle added depth Wednesday by signing free agent tight end Kellen Davis and releasing linebacker Allen Bradford. Davis will be the third tight end on the roster and his signing was made necessary by a slight injury suffered by rookie tight end Luke Willson against the Panthers. Carroll did not specify Willson's injury, but said it highlighted the need to add another tight end.
Davis played five seasons with Chicago and last season had 19 receptions for 229 yards and two touchdowns.