Olsen, a three-time Pro Bowl selection who has played 13 NFL seasons, said he's still interested in playing in the NFL.
"At this time I have not closed the door on any potential career options," Olsen wrote Thursday as part of a post on Twitter. "I still have the love of football in my heart and will explore all opportunities presented to me."
Olsen's agent, Drew Rosenhaus, told ESPN's Adam Schefter that he "will be in communication with other teams after the Super Bowl."
The decision to part with the Panthers was made after the 34-year-old Olson talked with general manager Marty Hurney about his future with the organization.
"The team and I are both on the same page that it is best we go in different directions for now," Olsen said in a statement released by the team. "On the field, I will always cherish the nine seasons we shared together. The wins, the losses, standing at midfield holding the Halas Trophy as NFC champs. The reality of going to the Super Bowl was beyond words, as was the disappointment of falling short."
The Panthers have a first-year coach in Matt Rhule, while star middle linebacker Luke Kuechly announced his retirement earlier this month.
Olsen's cap number for the 2020 season was to be $11,675,000, after he ruled out an extension to lower that number.
After dabbling in broadcasting, Olsen returned to the field this past season to prove he still could be among the top tight ends in the league. From 2014-16, he became the first tight end in NFL history to have 1,000 yards receiving in three straight seasons.
"The best part of playing in the NFL are the relationships," Olsen wrote. "I have been surrounded by the best teammates I could have asked for. Lifelong friends that are truly my brothers. Through the wins and losses, we have formed a bond that will last the rest of our lives.
"... Thank you to the fans. Panther Nation was always great to me. I heard all the cheers. I saw all the 88 jerseys. Just know I appreciate you all and you made it fun to be a Panther."
The only thing that slowed Olsen since Hurney acquired him for a third-round pick in a 2011 trade with the Chicago Bears was a foot injury that forced him to miss 16 games in 2017 and '18.
Olsen, the 31st pick by the Bears in 2007, had 52 catches for 597 yards and two touchdowns this past season. He has 718 career catches for 8,444 yards and 59 touchdowns.
Olsen holds the franchise record for most receiving yards (1,104 in '15) and receptions (84 in 2014) in a season by a Carolina tight end.
"I gave this team my all and in return you did too," Olsen wrote. "Regardless of what path we choose, I will always be a Carolina Panther."