The NFL is examining 10 separate incidents in which Jones was questioned by police since being drafted, including a February triple shooting at a Las Vegas strip club.
Fisher said Jones failed to inform team officials about two arrests in Fayette County, Ga., last year, including one related to a search for drugs at the home Jones bought for his mother.
"Typically speaking, if there's a situation like this, it's the player's responsibility to inform the club and that did not take place," Fisher told reporters Friday.
Worrick Robinson and Manny Arora, Jones' attorneys, said on a sports talk program on WGFX 104.5 The Zone on Friday that they didn't expect the player to be charged in the Las Vegas incident, but acknowledged that their client too often is in the wrong place at the wrong time.
"If he doesn't commit to changing it, at some point it's going to be too much," Arora said. "It may already be there to some extent."
Fisher and chief operating officer Steve Underwood met with Jones' lawyers at the attorneys' request earlier in the day for what Fisher characterized as an information-gathering meeting.
Fisher said the Titans are still gathering their own information before deciding whether to keep Jones on the roster. He said Jones must be cleared of legal problems before he can return to the team.
"As an organization it's always been our policy to gather facts and to make sure we have all the information, and that's what we're doing," Fisher said. "At this point, I don't see him coming back on the 19th."
Jones didn't participate in offseason conditioning last year after being questioned about his presence at a gas station in April when gun shots were fired. Jones, who instead spent time working out in Phoenix on his own, was never charged in connection with that incident.
Fisher told the radio program earlier this week there have previously been rumors about Jones' involvement in various crimes that turned out to be false.
But teammates are expected to be honest with each other, the coach said.
"Once that trust is violated on a repeated basis, one can come to their own conclusions," he said.
If Jones is released, the hole left by Tennessee's top defensive player will add to the team's already long list of needs. The Titans are in need of a running back and wide receivers after releasing Travis Henry, Drew Bennett and Bobby Wade, as well as help at cornerback and on the defensive line.
Fisher said receiver DontÃ© Stallworth, linebacker Ryan Fowler and cornerbacks Nick Harper and Jamar Fletcher have visited the Titans this week, but did not indicate if any offers had been made. He said team officials would meet with more players next week.
Fisher cautioned that fans shouldn't get frustrated because no high-profile players have been signed yet. He said he expected a few of the holes would be filled going into next month's draft. "Just because you have a lot of cap room doesn't necessarily mean you have to go out and overspend for a player," Fisher said. "We're watching the market. We're watching the money that's being spent. We're very aware of the players that are still available."