Rumours were rife ahead of Saturday's Championship clash between the two east midlands rivals that the Rams were preparing a bid for the 26-year-old striker, who has previously been on loan at Pride Park and who is out of contract at the end of the season.
But after his side's 1-1 home draw against Forest, in which Blackstock came on as a 63rd-minute substitute, Clough said: "We had a little chuckle over that (the report).
"Funnily enough, we did not go straight into the Forest dressing room after the game and make an offer for him."
Blackstock scored three goals in nine appearances during a loan spell at Derby in 2005 while he was playing for Southampton.
He has been at Forest since arriving at the City Ground from QPR in 2008.