In an interview on CBS' NFL pregame show, the oft-troubled cornerback said that not only does he expect to play football next season, "I think I might be back in Dallas."
Host James Brown then asked: "And you have an inkling that Jerry Jones will give you another shot?"
Jones grinned and said, "Yeah, I do," but didn't offer any details to back his assertion.
Cowboys spokesman Rich Dalrymple said the team had no comment.
Dallas released Jones on Wednesday after a turbulent season in which he was suspended six games for an off-field scuffle and made little impact on the field.
The Cowboys had traded for Jones despite the cornerback's suspension for the 2007 season after multiple incidents while with the Tennessee Titans. On Oct. 7, Jones got into a scuffle with a bodyguard who was part of a team-employed security detail.
The 25-year-old Jones spent part of his time away from football taking part in an alcohol rehabilitation program.
Flanked by lawyer Robert Langford, Jones was interviewed Saturday via satellite from California. He insisted his troubles were behind him.
"I did have an alcohol problem, but I have addressed the alcohol problem and went to AA," he said. "I went there for 2 1/2 months, going to AA every other week, seeing my counselors every day. Regardless ... I'm doing whatever it takes for me to change my life as a man, you know. Football, I'll always love football and always want to play football, but I still got to take care of myself as a person also."
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