The terms of Goodell's new deal, if reached, would be similar to his current contract which expires in 2019, according to the Sports Business Journal.
The 58-year-old Goodell succeeded Paul Tagliabue in September 2006.
The former PR man earned $32M in fiscal 2015 and more than $210M during his 10 years as commissioner.
The contract negotiations were first reported by Sports Business Journal.
Kaplan reports that the contract structure will include "a few million in base salary with bonuses to be determined" by the competition committee owners.More news: What happened between Jon Lester and Chris Bosio
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The deal is expected to be five years in length, which would keep Goodell at the league's helm through at least the 2024 season, per Monday's report.
If the National Football League eventually comes to terms with Goodell soon, New England Patriots fans will have the chance to personally congratulate the man who used his unilateral discipline authority to suspend Tom Brady on Thursday, Sept. 7 when he visits Gillette Stadium for the season opener.
Since the agreement was signed, the players union has clashed with Goodell and the league in notable cases such as Ezekiel Elliott's suspension for alleged domestic violence, Tom Brady's Deflategate suspension and Adrian Peterson's suspension for child abuse.
NFL Players Association executive director DeMaurice Smith told The MMQB last week that an NFL strike or lockout in 2021 is 'almost a virtual certainty'. One issue Smith says he will be focused on is Goodell's authority in disciplining players.