Defender Richard Keogh, midfielder Jeff Hendrick and striker Conor Sammon have been included in Giovanni Trapattoni's squad for the friendly against Poland at the Aviva Stadium in Dublin on Wednesday, February 6.
All three players have represented the Republic at Under-21 level but this is the first time they have been named in the senior set-up.
Rams boss Clough told the club's official website: "We're thrilled and extremely proud that Richard, Jeff and Conor have all received call-ups and it's obviously big news for us as a club to have three players selected in one international squad.
"In their own ways they have all contributed to what has been a very positive season so far on the pitch, and it's extremely pleasing to have our players' performances recognised with international call-ups.
"Richard and Conor have made big impacts since arriving in the summer and Jeff has firmly established himself in our midfield over the last year after coming through our academy, with his performances in recent weeks being as good as we've seen from him in a Derby shirt.
"They are all extremely good characters to have around the place and it goes without saying the call-ups are all richly deserved.
"We'll all be watching with interest next month and we have no doubt they'll do themselves, and the club, proud.
"It's a good chance for all of them to try and impress during their short time away and keep themselves in the Ireland set-up moving forwards.
"It'll be a great experience for all three of them, there's no doubt about that and hopefully we'll reap the benefits of that as well."