"I've had discussions with the committee chairman, but received no "notices", Jones said during his weekly appearance on CBS Sports Radio's 105.3 The Fan in Dallas.
The range of punishments, according to the Times, includes fines, docking draft picks and even suspending Jones, who has owned the Cowboys since 1989.
Jones was removed as an ad hoc member of the committee when he brought up the possibility of legal action.
The Compensation Committee now consists of Falcons owner Arthur Blank, Chiefs owner Clark Hunt, Giants co-owner John Mara, Patriots owner Robert Kraft, Steelers owner Art Rooney II, and Texans owner Bob McNair.
"Roger has nearly 18 months [left before the contract expires]", Jones said. "We've got all the time in the world to evaluate what we're doing, and all the time in the world to extend him".
Belson's latest article also mentions something that PFT has consistently reported, and that others in the media have pooh-poohed: Some owners believe that Jones instigated Papa John's CEO John Schnatter to publicly disparage the league during a recent earnings conference call, blaming reduced corporate revenues on the NFL's current controversies and ratings declines.
There is thought that Jones' motivation comes out of anger with Goodell giving Dallas' star running back Ezekiel Elliott a six-game suspension that he finally started serving last week.