Should Jones proceed with his appeal, the hearing would go before Goodell, Judy Battista of the NFL Network reported, citing a source informed of the situation.
It is not immediately known when the hearing would take place.
NFL owners are citing a rule -- Resolution FC-6 -- that was introduced in 1997 that says if an owner participates in bringing litigation against other owners, he must reimburse them for the legal fees.
The New York Times on Monday reported several owners support the fine against Jones and that the commissioner pursued the action after they "believed that Jones had crossed an unspoken boundary by threatening his colleagues."
In November, Jones said he was prepared to sue the six owners serving on the league's compensation committee.
Jones eventually backed down on his threats of a lawsuit but during a league meeting in December, he was criticized for his behavior by other owners. Most of those owners agreed to give Goodell a five-year extension that could pay him as much as $200 million.
Elliott was suspended in August and Jones said he did not deserve to get penalized for an incident that occurred while at Ohio State. After a back-and-forth court battle, the second-year running back's on-again, off-again suspension was reinstated on Nov. 9. Three days later, Elliott accepted the punishment.
While Elliott was appealing, Jones was trying to persuade league owners that Goodell's contract extension should be significantly less than what was proposed, the Times said.