With the Redskins already out of the race for the playoffs, Shanahan is considering the possibility of resting Griffin for the remainder of the season in an attempt to protect the 23-year-old from injury.
Griffin spent much of this year's off-season recovering from a serious knee injury and, having been sacked 24 times in the last five games, Shanahan is worried that the quarterback could suffer another major setback soon.
The 2012 offensive rookie of the year would be replaced by Kirk Cousins in the side, with Shanahan likely to make his decision later today.
Snyder, whose relationship with Shanahan has been the subject of much debate recently, will not intervene in the decision either way, according to ESPN.
The Redskins are currently bottom of the NFC East with a 3-10 record having won the division last season.