The Browns designated Griffin to return from injured reserve on Wednesday morning. The team now has 21 days to decide whether he will return to the active roster. If he doesn't, he will remain on injured reserve for the rest of the season.
Griffin was the second quarterback throwing in drills open to the media. Josh McCown took the first reps, with Griffin up second.
He threw freely but not always accurately, as a couple of throws were wide. In all drills the media saw, quarterbacks either threw to staff members standing in one spot or to receivers running without defensive backs.
Griffin will not play in Sunday's game against the New York Giants. Coach Hue Jackson all but ruled him out on Monday, saying "right now it might be a little bit early" for Griffin to play.
Griffin has been out since the season opener against the Philadelphia Eagles, when he broke the coracoid bone in his left shoulder.
In that 29-10 loss, Griffin completed 12 of 26 passes for 190 yards and rushed for 37 yards.
Five quarterbacks -- Kessler, McCown, Griffin, Charlie Whitehurst and Kevin Hogan -- have played for the winless Browns (0-11) this season. Wide receiver Terrelle Pryor, a converted quarterback, has thrown nine passes, completing five.