Johnson is scheduled to make $8 million in 2014 and it was expected he would be released if the Titans couldn't find a trade partner. He told The Tennessean earlier this year that he believes he has been underused in the Titans' offense and said he would be open to a trade.
ProFootballTalk.com earlier reported that the Titans were receiving trade interest for Johnson.
Johnson, who also told The Tennessean he played the majority of last season despite a torn meniscus in his knee, underwent surgery in January.
Titans general manager Ruston Webster repeated Tuesday on "The Midday 180" that there is no ticking clock for a resolution.
"We are kind of going through our options now, working through that," Webster said. "My job as GM is to do my due diligence and make sure that whatever it is, it's the right thing. And that's just what we are trying to do. We'll see where it goes. There is no real timetable, but I will say this: I know for Chris' sake I would like to make it work sooner rather than later."
Johnson, who had 358 carries when he rushed for a franchise-record 2,006 yards in 2009, ran just 279 times for 1,077 yards in 2013 -- the second-lowest total of his six-year career.
The 279 carries marked Johnson's highest total in his three seasons under Mike Munchak, who was fired as coach after the season. Johnson had more than 300 carries in each of the previous two seasons before Munchak was hired.
Johnson, 28, has rushed for 7,965 yards and 50 touchdowns in his career. He also has 272 catches for 2,003 yards and eight touchdowns.
ESPN.com Titans reporter Paul Kuharsky contributed to this report.