The striker finished the season on loan at Pride Park from Norwich, where his contract expires next month.
The Championship club have been in talks with Martin, 24, and his representatives and Clough are confident of adding the player to the squad on a permanent basis.
"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.
"Some of his link-up play with Jamie Ward and the midfield against Millwall on Saturday was very good. We have seen some good things from him."
Martin joined Derby on loan in February and made 13 league appearances for the Rams, scoring two goals.