Jones, who became a free agent when the Cincinnati Bengals declined to pick up the 2018 option on his contract in March, told SiriusXM NFL Radio on Tuesday that he's fully recovered after undergoing groin surgery following the season.
"I had groin surgery the week after the Super Bowl," said Jones. "I'm finally 100 percent from that, just got cleared by the doctors. Running full speed. Have been in contact with several teams, I expect it to pick up in the coming weeks."
The Bengals did leave the door open to bringing back the 34-year-old Jones, with the team saying it would consider re-signing Jones as a nickel back and kick returner.
Jones has played 11 NFL seasons, the last eight with the Bengals. He did tell the team's website in March that he would "love to come back."
A one-game suspension at the start of the season for violating the league's personal conduct policy and injuries limited Jones to nine games in 2017, all as a starter.
Jones was a first-team All-Pro selection in 2014 and was a Pro Bowl selection in 2015.
Jones has been involved in a number on-field and off-field incidents, however, and that includes a misdemeanor charge from an altercation that led to his one-game 2017 suspension.
He also was suspended for the 2007 season and part of the 2008 season for violating the league's personal conduct policy.