Shanahan, speaking on ESPN's "Sunday NFL Countdown," said he was surprised by Cutler's troubles but not as much by Griffin's. The latter has dealt with two leg injuries in his first three seasons, plus is learning a new system under first-year coach Jay Gruden.
As for his own future, Shanahan said he does want to coach in the NFL again but only for a team that will make a strong commitment to winning.
Shanahan said Griffin, whom the Redskins drafted second overall in 2012, could be a franchise quarterback.
"He has that ability," Shanahan said. "He's in charge of that himself, though. It takes a lot of work, a lot of studying. ... He can be as good as he wants to be. But he has to make a commitment in that film room like he's never done before."
The Redskins fired Shanahan after last season, his fourth in Washington and his second with Griffin. Their last season was full of stories speculating on the nature of their relationship. The stories intensified once it became apparent the Redskins likely would fire Shanahan.
But being free of Shanahan hasn't resulted in a lot of success for Griffin. He started the first two games, but dislocated his ankle early in the second one and missed six games. Griffin was then benched after three starts and regained the job this past week when Colt McCoy suffered a season-ending neck injury.
Griffin helped the Redskins beat Philadelphia, 27-24, on Saturday. It represented the first time he had started and finished a win in nine games, dating to Week 9 of 2013.
Griffin went from a system that relied heavily on play-action and one that adopted some of what he did at Baylor to one that was focused more on dropping back and staying in the pocket.
"Anytime you get in a new system, it takes some time," Shanahan said. "When you take a look at Robert trying to make the transition to more of a dropback quarterback, there's a process and it doesn't happen overnight. It will take some time. But you could see yesterday he felt much more comfortable. He played well. But this is an ongoing process. One key to the quarterback position is to get comfortable with that pocket, especially when pressured, being able to slide and step up side to side. That doesn't happen overnight."
As for Cutler, Shanahan drafted him while in Denver and spent three years with him. The Broncos fired Shanahan and then traded Cutler to Chicago. The Bears benched Cutler this past week.
"I'm surprised," Shanahan said. "Anytime you're not with an organization it's hard to say what Jay Cutler has done. I just know being with him in Denver that he's got all the intangibles. Now, can you get that out of him? I really believe in Jay but he has to make a commitment that he's going to get better and better. It's going to be a group decision to get him over the top, but he is a franchise-type quarterback."
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