He suggested he was at odds with the compensation committee chairman, Atlanta Falcons owner Arthur Blank.
Blank is the head of the NFL's Compensation Committee, and is one of the key players in Goodell's negotiations.
Roger Goodell (right) is reportedly seeking $49.5million per year, a private jet for life and health insurance for his family to stay on at the NFL.
The New York Times reported over the weekend that the committee will meet Monday to discuss Goodell's new contract, a discussion that has taken on a new edge since Dallas Cowboys owner Jerry Jones has voiced his displeasure with Goodell's role in shaping the current state of the league.
According to King, Jones' demands over Goodell's contract have not gone over well with the competition committee.
Goodell, whose proposed contract with the NFL now is undergoing an approval process, asked the league's compensation committee in August to raise his salary from $30 million to $49.5 million per year, ESPN reported Sunday.
Jones said that he isn't pushing for a review of Goodell's contract because the commissioner suspended Cowboys running back Ezekiel Elliot six games on allegations of domestic violence.More news: Corvette unleashes the 2019 ZR1: The most powerful 'Vette ever
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"I've been dealing with this commissioner for nearly 28 years, as an employee of the NFL", Jones said on his radio show late last week.
The NFL Competition Committee is meeting today to discuss extending the NFL boss's already lucrative contract.
Goodell suspended Elliott following a yearlong investigation by the league after prosecutors in OH declined to pursue the domestic violence case, citing conflicting evidence.
Some fans have said protests are disrespectful to the American flag and to the military, and have boycotted the NFL.
Despite NFL protests, which have resulted in a ratings slide, team owners will look to Goodell to play a key role in leading the league through the next collective bargaining agreement and broadcast contract cycle.
"It's about concussions, Jones vs. Goodell, [Ezekiel Elliott's suspension], the anthem".
"But there is nothing in the book, like standing for the anthem". A source told King that members of the committee were going back to owners with details of the proposed deal for Goodell to gauge their reactions.