Both sides are still committed to finalizing a long-term extension prior to the July 15 deadline, ESPN's Adam Schefter reports.
Tennessee placed the non-exclusive tag on the star tailback in March, a day after re-signing quarterback Ryan Tannehill to a four-year, $118-million contract.
In 2019, Henry led the NFL with both 1,540 rushing yards and 16 rushing touchdowns. He added another 446 yards and two touchdowns in the Titans' postseason run to the AFC Championship Game.
"I think any time a player, when you have to use the tag on them, that's something that ideally they probably don't want," Titans general manager John Robinson said Wednesday, according to team writer Jim Wyatt. "But still, at the same time, I know that he wants to be a part of this football team and I thought it was good that they communicated back he does want to be here, and he does want to keep working on this thing. It wasn't something like, 'OK, well, I'll take the (tag) and I'm done, or I am just going to do whatever.' He wants to be here, and he conveyed the message to me, through his agent, that he wants to keep working on this thing and we do, too."