Davis, 35, wanted to retire with the Carolina Panthers, the team that made him the 14th pick of the 2005 draft. The three-time Pro Bowl selection is the team's all-time leading tackler (1,094) and in 2012 became the first player in NFL history to successfully overcome three anterior cruciate ligament tears in the same knee.
Davis also was a team captain the past eight seasons and the 2014 Walter Payton NFL Man of the Year Award winner for his foundation's community work with kids in North and South Carolina, as well as his home state of Georgia.
The Panthers, looking to get younger and faster on defense in 2019, told Davis in January they were going in another direction at linebacker and he would not be re-signed. Davis responded with an emotional video on social media.
"Carolina is going to always be home for me and my family, but I'm not retiring,'' Davis said. "I feel like I have way too much football left in me to walk away from the game right now, so I want to keep playing. I'm going to keep playing.
"Hopefully, someone is going to give me that opportunity.''
Davis had planned to make the 2018 season his last, but he had a change of heart after the NFL suspended him for the first four games for violating the league policy on performance-enhancing drugs.
ESPN's David Newton contributed to this report.