Per The Athletic's Ben Standig, Rhiannon Walker and others, a source at Nike said the company "anticipates a change soon."
Nike hasn't issued an official statement, but the company has removed Washington merchandise from its official website.
The Nike source noted the change is anticipated in part "because it would take time for them to remake the jerseys and provide them to distributors."
There has been increased pressure on Washington to change its nickname. FedEx, which sponsor's the team's stadium, requested the team make a change.
"We have communicated to the team in Washington our request that they change the team name," the company said in a statement, via ESPN.
Washington issued a press release Friday, announcing it would be conducting a "thorough review of the team's name" after having initial conversations with the NFL "in recent weeks."
The franchise has used the nickname since 1933 when it was based in Boston and retained it after moving to Washington, D.C., prior to the 1937 season.