According to ESPN.com's Cameron Wolfe, Mularkey suggested Tennessee wasn't in the market for Kaepernick since he didn't know the team's offense: "I'm not aware if there was [interest]. I know he's not familiar with our offense. I know T.J. Yates had some experience with it in Atlanta and with us for a couple of weeks."
Mularkey noted that his offensive scheme is similar to that of Dallas Cowboys offensive coordinator Scott Linehan's, and Weeden played under Linehan in 2014 and 2015.
Weeden beat out Yates, Matt Barkley and Matt McGloin, and Mularkey noted that the former Cleveland Browns first-round pick had an immediate leg up in the competition: "As quickly as we could get somebody up to speed in a short amount of time, he had the advantage over everybody."
The Titans were in the market for a quarterback behind veteran backup Matt Cassel since Marcus Mariota suffered a hamstring injury and is uncertain for Week 5.
Kaepernick has remained unsigned since opting out of his contract with the San Francisco 49ers during the offseason.
A major point of debate has been whether Kaepernick's decision to protest during the national anthem last season is a bigger reason for his absence from an NFL roster than his on-field play.
The 29-year-old veteran went just 1-10 for the Niners last season, but he threw for 2,241 yards, 16 touchdowns and four interceptions while rushing for 468 yards and two scores.
Kaepernick has a career record of 28-30 as a starter, and he has two NFC Championship Game appearances and one Super Bowl appearance to his credit in a starting role.