If he doesn't start, then Gruden said Colt McCoy would do so against Dallas for the teams' Oct. 27 matchup. Griffin has not played since dislocating his left ankle in Week 2.
As of now, Gruden sounded as if McCoy starting would be the likely scenario, considering that Griffin has yet to fully practice.
"He still has a long ways to go to show that he can play," Gruden said, "to show that his ankle is 100 percent. He has to be 100 percent ready to go. We don't want to put him out there at 85 percent, have it be weak and have him do something else to it. We want to make sure he's ready to go when he's out there."
It's the second time Griffin has returned from a serious leg injury in his three seasons. His slogan after his 2012 knee injury and subsequent surgery was "All in For Week One" and he ended up starting the season opener.
Griffin's return led to friction and miscommunication between him and former coach Mike Shanahan. There's no catchy slogan this time, nor has Griffin talked about his recovery.
For Gruden, he just wants to make sure Griffin can do what Washington needs him to, physically and mentally.
"Robert has to be honest with himself in how he's feeling," Gruden said. "He has to get out there and run around. We'll give him more this week and see where he's at. But can he cut without pain? Can he run without pain? Is he full speed? Is it sturdy enough? Does he play good with the brace on? There's a lot of issues that still go into making him the starter or seeing if he's ready or not."
Gruden said Griffin still must be cleared for a full return to practice. He said the trainers and doctors must feel comfortable with Griffin playing. And then the quarterback has to feel as if he's ready.
"If he says yes, then I have to feel comfortable putting Robert out there in the game," Gruden said.
If he doesn't start Monday, then it appears Griffin's return would come the following week at Minnesota. That would give him eight weeks to show the Redskins his progression as a quarterback. Washington must make a decision on him in the spring regarding a fifth-year option.
McCoy's ascension was a result of Kirk Cousins' downfall. Cousins threw nine interceptions in his five starts this season. He fumbled and threw an interception in the first half of Sunday's 19-17 win against Tennessee before being benched.
McCoy completed 11 of 12 passes for 128 yards and a touchdown, driving the Redskins for the last-second, game-winning field goal.
"He does have great intangibles," Gruden said of McCoy. "He's a very good competitor. I feel like he'll get us in the right play and make the right throw. I've always liked his demeanor. He has the intangibles to be a good quarterback. He has a great opportunity Monday."
Colt McCoy Named Redskins' Starting QB
The "NFL Insiders" crew reacts to the Redskins' decision to name Colt McCoy the starting quarterback.