Wednesday's report comes after Schefter and Chris Mortensen relayed word Sept. 17 that Dallas Cowboys owner Jerry Jones attempted to halt negotiations.
According to Schefter, Jones "raised issues about the deal, and wanted to open up the search during the process."
Jones' qualms with Goodell's new deal weren't specified, and he later denied he was trying to stall the process.
"All of that is without any substance at all," Jones said, per Schefter and Mortensen. "The exercise of looking and extending our commissioner's contract is one that we keep really in tight. So there certainly are exaggerations there; that's not the way that works. I've always supported Roger, and let's just leave it at that."
Goodell, who started serving as commissioner in 2006, is currently under contract through 2019. According to Schefter, Goodell has reportedly earned north of $21 million annually on average based on the NFL's public disclosures of his compensation.
The league's most recent filing reportedly showed Goodell earned a shade over $31 million in 2015—down from roughly $34 million the year prior.