Cannon, 33, had minor knee surgery after the Texans’ organized team activities.
Cannon joined the Texans in a trade from the Patriots in March. As a cancer survivor, he opted out of the 2020 season because of COVID-19 concerns.
In nine seasons with the Patriots, Cannon played 115 games and started 69 of those.
Taylor, 31, signed a one-year deal with the Texans in April. He played only one game for the Packers in 2020, tearing an anterior cruciate ligament after only 63 offensive snaps in the season opener.
Taylor played only two games — 114 offensive snaps — in 2019 because of a torn biceps.
The Texans also cut long snapper Mitchell Fraboni, who signed June 14.