The sixth-year back who some believe is in decline, has averaged 4.6 yards per carry since he was drafted in the first round out of East Carolina, including a 2,006-yard season in 2009, his second year in the league.
Johnson, 28, rushed for 1,077 yards on 279 carries -- a career-worst 3.9 yards per carry last season after posting 1,243 yards on 276 carries in 2012.
Johnson, who had minor knee surgery in January, said he was underused in the Titans' offense and is open to being traded. Johnson turns 29 in September with more than 2,000 career touches in six seasons.
Johnson is owed $8 million in 2014 and made $30 million in salary and bonuses the past three seasons.
Coach Ken Whisenhunt and general manager Ruston Webster are not in a hurry to dump Johnson. There are no deadline dates in his contract -- roster or workout bonuses that would warrant his premature release -- but if a deal cannot be found during or after the draft, it's likely he would be released.
"I can't speak about what he has left in the tank, you never know. I know he's there every Sunday. He practiced every day from what I've seen looking at the (participation) charts," Whisenhunt said last month at the 2014 NFL Scouting Combine. "It's a process with everybody you go through with the football team. ... Putting together the team is no exact science. Certainly chemistry will be a part of it. We're under no deadline to do it."
Webster said the Titans would "take a look at what's out there" at the running back position starting this week at the 2014 NFL Scouting Combine.
"I think we can be as patient as we want to be," Webster said.
Arizona, Oakland, Miami and Cleveland were hinted at as potential landing spots for Johnson, but no team is likely willing to take on Johnson's immense salary. Considering he has 2,014 career touches (272 receptions, 1,742 carries), teams would sooner look to the draft, where a late first-round pick would require only a four-year deal worth approximately the same $8 million Johnson is owed for next season.
The Browns are in need of a running back and former Titans offensive coordinator Dowell Loggains joined the Cleveland coaching staff in January.