The 33-year-old, who has previously been on loan with the Championship club, is available on a free transfer after leaving Watford at the end of last season.
Clough told the Derby Telegraph: "John is training with us. He has a couple of playing offers from clubs but we have said 'come and train with us for a couple of weeks' and see how it goes. He is a player we have liked for two or three seasons."
Eustace made nine appearances during a loan spell with Derby in 2009.