Jones' contract will not expire until the start of the league year on March 14, at which point he will become an unrestricted free agent and will factor into the compensatory pick formula next year.
However, that doesn't rule out a potential return to Cincinnati. According to the team website, the Bengals told Jones they would like him back to compete as a nickel corner and a kick returner.
"Of course I'd love to come back," Jones told the team website on Friday. "Don't make it sound like I'm ready to get out of there because I'm not. I'm very thankful to everyone there, Coach [Marvin] Lewis and Mr. [Mike] Brown. Of course, you know me. I'd love the chance to get on the field and compete every play, every down. Obviously I've got some things to sit down and think about the next couple of days with my family."
Jones, 34, was set to count $6.9 million against the salary cap this season and played in only nine games due to a combination of injury and a one-game suspension for a violation of the NFL's personal conduct policy due to an arrest last January.
Jones was placed on injured reserve in December after injuring his groin while making an interception -- his only one of the season -- against the Pittsburgh Steelers. He finished the season with four pass deflections. He was also one of the team's kick returners and had a punt return for a touchdown that was called back due to a penalty earlier in the season.
Jones was arrested last year on Jan. 3, the first day of the Bengals' 2017 offseason, for allegedly pushing a security guard and failing to comply with law enforcement.
A video from the back of a cop car showed Jones going on a tirade against the arresting officer and telling him "I hope you die tomorrow." Jones was suspended by the NFL for the Bengals' season opener after the incident.
He was charged with misdemeanor assault, disorderly conduct and obstructing official business, along with a felony charge of harassment with a bodily substance for spitting on the hand of a nurse while being booked into injury.
The prosecutor declined to pursue the felony charge and all other charges were dropped except obstructing official business, to which Jones pleaded guilty.
Jones, who joined the Bengals in 2010, turned his career around in Cincinnati after it almost ended when he was suspended for the entire 2007 season after an incident in a Las Vegas nightclub that resulted in a man being paralyzed. Jones was later ordered to pay $12 million in damages to the victim.
Jones, a 2005 first-round pick for the Titans, spent one season in Dallas before signing with the Bengals and eventually earned a starting role there. He was named a team captain for the first time in his career during the 2016 season.