Asked about the topic on 670 The Score's McNeil & Parkins Show, Rivera said it was "a discussion for another time."
"It's all about the moment and the timing," he said. "But I'm just somebody that's from a different era when football wasn't such a big part of the political scene. That's one of the tough things, too, is I've always wanted to keep that separate."
Rivera added that he supports the wider social justice movements and his players' participation in them but that "it's all about the timing and the best time to discuss those things."
Critics have long argued that Washington's moniker is racist. The subject has received renewed attention as Americans protest against systemic racism and police brutality.
On Tuesday, Washington removed former owner George Preston Marshall from its Ring of Fame, per ESPN's John Keim. The team was the last in the NFL to integrate, with Marshall finally doing so amid pressure from the federal government.
"All the other teams we play have Negroes; does it matter which team has the Negroes?" he once said.
Before that, the team announced it plans to retire the No. 49 jersey of Bobby Mitchell, the first Black player to suit up for Washington. Mitchell's name will also grace FedExField's lower level, replacing that of Marshall.
Removing Washington's nickname has remained off the table, though.
Team owner Daniel Snyder told USA Today's Erik Brady in 2013 that Washington "will never change the name of the team." He explained to ESPN's John Barr in 2014 the nickname "really means honor, respect."