Griffin has endured a disappointing campaign this year having overcome a serious knee injury during the off-season, leading the defending NFC East champions to just three wins from their 13 games.
The 23-year-old has been sacked 24 times in the last five games and 38 overall this season, and Shanahan admits that he is thinking about resting Griffin for the final three matches in order to protect him against further injuries.
"I've got to do what's best for the organization. If we feel the best thing for the organization is doing that for Robert, then hopefully Robert will understand why we're doing it," Shanahan told reporters.
"We're doing it because he's a franchise quarterback and we want him to be able to go into the off-season and get full preparation and be ready for next year rather than playing one of the next three games and all of a sudden he sets himself back with a possible injury, whatever that may be."
The Redskins are already out of the NFL playoff race and face the Atlanta Falcons, who also have a 3-10 record for the season, on Sunday.