Jones will see other specialists before deciding whether to have surgery, Hunter said. An operation wouldn't necessarily end the cornerback's career.
"It looks very promising for him," Hunter said. "Do not ever count this man out. He is going to be back."
Jones, a fourth-year pro with a history of off-the-field trouble, received a second chance from the Bengals in May when they signed him to a two-year contract.
Jones' repeated run-ins with the law led to him being suspended for the 2007 season while with the Tennessee Titans for violating the league's personal-conduct policy. The Titans, who drafted Jones in the first round in 2005, traded him to Dallas during the suspension, and he played nine games with the Cowboys in 2008 before he was suspended for six games after an alcohol-related scuffle with a team-provided bodyguard. He was released and sat out the 2009 season.
Jones made 14 tackles, one forced fumble and one interception in 2010.
"He's learned to channel that energy in the right direction," Hunter said. "That's why I'm even more optimistic, as Adam is, that he's going to bounce back and be fine. Indications are that he's going to be OK."
The Associated Press contributed to this report.