And it's easy to understand the rumors given Johnson's declining numbers since his 2,000-yard season in 2009.
But the Titans would be wrong to make that move right now.
Coming into Week 4, Johnson was running at a 1.2-yard clip.
But in Sunday's loss to the still-unbeaten Texans, the veteran Johnson carried the ball 25 times for 141 yards. That's nearly five yards per carry against a defense that was shutting down opponents through the first three weeks of the season.
There's no reason to think Johnson won't put a handful of those games this year.
In football speak, Johnson is three years to the good side of 30. In English, we call that 27.
He has two to three solid years left in him and this team has four, maybe up to six, wins in them this year.
That means Johnson will finish the year somewhere around 1,000 yards again, enough of an impact player to give the passing game some breathing room.
It also means that the Titans will finish in the middle (maybe lower middle) of the pack and that gives them few good options on draft day 2013.
The only surefire first-round running back at this point is South Carolina's Marcus Lattimore, who is projected by most scouts as a top-25 guy.
The rest of the talent at running back is second- to fourth-rounders.
This may not be your father's NFL anymore. And pass-happy offenses may be the hot commodity in the NFL, but eventually, the team that runs the ball and defends the run wins the big game.
The Titans would be foolish to part with Johnson at this time.
Lou Rom covers the NFL and whatever else gets under his skin for Bleacher Report. Follow him on Twitter at louromlive.