The Sweden international's current deal came to an end after the Rams game with Queens Park Rangers, in which Stoor was forced to come off after picking up a black eye.
Clough is looking to keep the player at Pride Park until the New Year.
"His eye completely closed," said Clough to Sky Sports.
"If you have seen the Rocky films, you'll know what I mean.
"He has a good black eye and there was no way he could continue but we are looking to extend his loan."