Sixth-round DT Kalia Davis will also begin camp on the non-football injury list, per Lynch.
Verrett is coming off a torn ACL, while Woerner has a core muscle injury and Davis has a knee injury.
Verrett, 30, was taken with the No. 25 overall pick back in 2014 by the Chargers. He finished his four-year rookie contract and played out 2018 under the fifth-year option for $8,526,000.
Verrett landed on injured reserve for three consecutive years. He missed all of 2018 due to a ruptured Achilles. From there, he signed with San Francisco in 2019 and returned to San Francisco on another one-year contract in 2020.
He signed a one-year deal with the 49ers worth $5.5 million, with a chance to make $6 million had he made the Pro Bowl in 2021. San Francisco re-signed him to another one-year deal for 2022 after he missed the season with a torn ACL.
In 2020, Verrett appeared in 13 games for the 49ers and recorded 60 tackles, two interceptions, and seven passes defended.