Owner Daniel Snyder has said he will never change the team's nickname, but Monk and Green told WTOP Radio in Washington, D.C., on Tuesday that the topic isn't one that should be so easily dismissed.
"[If] Native Americans feel like Redskins or the Chiefs or [another] name is offensive to them, then who are we to say to them 'No, it's not?'" Monk told the radio station.
Monk, who was inducted into the Pro Football Hall of Fame in 2008 and is the Redskins' all-time leader in receptions (888) and yards receiving (12,026), added that a name change should be "seriously considered."
Green, a former cornerback who was also inducted into the Pro Football Hall of Fame in 2008 and is the Redskins' franchise leader in interceptions (54), agreed that a name change should be under consideration.
"It deserves and warrants conversation because somebody is saying, 'Hey, this offends me,'" Green told the radio station.
In May, 10 members of Congress sent a letter to the Redskins, the NFL and its other 31 teams, calling for a name change.
Commissioner Roger Goodell, however, defended the team's nickname in a letter to the members of Congress, writing that the Redskins name "is a unifying force that stands for strength, courage, pride and respect."
The nickname is the subject of a long-running legal challenge from a group seeking to have the team lose its trademark protection.
Information from The Associated Press was used in this report.