The 24-year-old joined the Rams in February this year on a loan basis from Norwich City until the end of the most recent Championship campaign.
With his contract at Carrow Road due to expire later this summer, Clough has been impressed enough to push through a permanent move for the striker.
We are close to securing Chris Martin," Clough told the Derby Telegraph. "I think he has shown enough in the last two or three months to say he is going to be a good addition for us."
Martin found the net twice during his 13 outings for Derby this season.