The Swiss defender has spent the last two weeks with the Rams and has featured in their last three pre-season friendlies.
Gjokaj, 18, linked up with Clough's side after a spell with Lucerne in the Swiss Super League.
"Everything about him has impressed us. He has shown a great attitude," Clough told the Derby Evening Telegraph.
"We threw him in against Mansfield, Burton and Northampton, and he has competed and looked comfortable.
"He is another good young player we would like to put into our system."