League spokesman Greg Aiello told NFL Network's Ian Rapoport that no final decision has been made on Goodell’s decision of whether to recuse himself.
The NFLPA made the request for Goodell to recuse himself on Tuesday.
The league announced last week that Goodell will hear Brady's appeal, which was filed by the NFLPA last Thursday.
The NFLPA called for Goodell to designate a neutral party to serve as an arbitrator in the appeal. In its request, the union said players feel "the commissioner's history of inconsistently issuing discipline against our players makes him ill-suited to hear this appeal in a fair-minded manner."
In hearing the case, Goodell will exercise his right under the league's 2011 collective bargaining agreement to hear Brady's case instead of either an independent or NFL-affiliated arbitrator.
Brady is appealing a four-game suspension handed down by the NFL for his role in Deflategate. The punishment came as a direct result of a report from attorney Ted Wells that suggested it is probable that Brady "was at least generally aware of... the release of air from Patriots game balls."
The Patriots were also fined $1 million by the league and lost their 2016 first-round draft pick and 2017 fourth-round pick.
On Tuesday, New England owner Robert Kraft told reporters he will not appeal the punishment and will "accept, reluctantly, what [Goodell] has given us."
- Molly Geary