He was eligible for the practice squad, and the feeling is that's where the Dolphins would put him if they wind up signing him.
But that does have anything to do with Griese? The Dolphins certainly won't say. They're just saying they're always on the lookout for good players, and they think Stoerner has potential.
Word is Griese could miss as much as a month because of the injury, which involves ligament damage to his left big toe.
That puts Sage Rosenfels in the role of backup for now, and the question is whether he's ready to handle that.
Yes, Rosenfels has looked good at times in the preseason and, yes, he has a stronger arm than any quarterback on the Dolphins roster.
But he also is very raw, and one can't help but remember his brief appearance against Green Bay last season when he looked totally overwhelmed.
One would hope he has progressed significantly since that time because the Dolphins could be in big trouble if he hasn't and Jay Fiedler gets hurt, which history has shown certainly could happen.
In the meantime, the Dolphins can only hope for a speedy recovery by Griese.