Dunne was released by Aston Villa at the end of last season, and while he could secure a move to another Premier League club, Clough is ready to act if he indicates that he is prepared to drop down to the Championship.
The 47-year-old told the Derby Telegraph: "We know that he's been released by Aston Villa, but we've heard that he wants to stay in the Premier League.
"He's that kind of centre-half we like. If the possibility became available down the line, we would look at it."
The Republic of Ireland international missed last season through injury.