After a three-hour practice Sunday, San Francisco coach Jim Harbaugh said the team is bringing in the 34-year-old Culpepper for a tryout on Monday.
"We're going to have Daunte in for a workout and kick the tires," Harbaugh said. "I'm looking forward to that."
Culpepper, the No. 11 pick in the 1999 draft, hasn't played in the NFL since an eight-game stint with Detroit in 2009. During an 11-year NFL career, mostly with the Minnesota Vikings, Culpepper has played in three Pro Bowls. He spent last season with the Sacramento Mountain Lions of the United Football League.
NFL Network's Jason La Canfora reports Culpepper has been contacted by several teams as he attempts a return to the NFL.
Smith and Kaepernick alternated most of the snaps Sunday during 11-on-11 drills in front of 8,200 fans at Candlestick Park. The 49ers were practicing on their home field as part of a full day of "Fan Fest" activities.
Smith felt right at home in a stadium he wasn't sure he'd ever play in again. He was a question mark to return to San Francisco after last season's disappointing 6-10 finish, but the NFL lockout and the 49ers' new coaching staff gave him another chance with the team.
"It was a great day to come up here before we play," Smith said. "The sun's out and it's nice and windy. That's really familiar."
Smith is also familiar with training camp competitions. This is his fourth since the 49ers chose him No. 1 overall in the 2005 NFL Draft.
Smith lost out to veteran Tim Rattay during camp as a rookie, but was handed the starting job in each of the next two seasons. In 2008, the 49ers allowed journeyman J.T. O'Sullivan to compete for the starting job under new offensive coordinator Mike Martz. O'Sullivan was San Francisco's opening-day starter that season.
Smith was beaten out by Shaun Hill in 2009. Smith regained the starting job midway through that season and was San Francisco's regular starter last season.
"Alex is No. 1 on the depth chart right now, and Colin is No. 2," Harbaugh said. "They're still competing. We'll determine it on who's practicing better and who's playing better."
Smith completed five consecutive passes on a practice-ending drive Sunday that was stopped short of the end zone. That drew boos from fans after Smith was denied on a fourth-down scramble at the 2-yard line.
Kaepernick had drawn cheers when he ended the previous session by connecting with tight end Delanie Walker in the corner of the end zone. The rookie said he feels no different about the competition than he did when Smith arrived for his first practice with the team on Aug. 4.
"From the start, (Harbaugh) said the best player is going to play," Kaepernick said. "We're both out there working hard and competing for that starting spot. Ultimately, it's going to be up to coach where the chips fall."
Undrafted rookies Jeremiah Masoli and McLeod Bethel-Thompson are the other quarterbacks on San Francisco's training camp roster.
The Associated Press contributed to this report.