The Rams will host Rovers over the weekend of January 26/27, meaning their Championship fixture away to Hull will have to be rearranged, after overcoming League One leaders Tranmere 5-0 at Pride Park on Saturday.
Derby drew 1-1 at home to Blackburn in the league in October and Clough is expecting another tough game.
He told the club's official website: "Blackburn, despite deciding to part company with manager Henning Berg at the end of last month, have been on a good run in the last few weeks and strung a few wins together.
"They proved when they came to Pride Park in October that they have some good players and it will be a difficult tie for us, but our form at home has been excellent this season and that will give us a great deal of confidence.
"It is a game to look forward to but in the meantime, we have got two important fixtures against Brighton and Nottingham Forest to play before we think too much about Blackburn."