Sky Sports reported on Wednesday that Ince, who thrived on loan at the Rams last season, was to hold talks with Hull over his future and that both Derby and their former manager Steve McClaren, now at Newcastle, are interested in his transfer.
Derby have so far signed Darren Bent from Aston Villa as well as Alex Pearce, Chris Baird, Scott Carson and young striker Shaquille McDonald from Cheltenham.
And Clement, who insists he is keen to keep adding quality to his squad, confirmed the clubs are in talks with Hull over Ince moving to the iPro Stadium.
“We’ve made five permanent additions so I think we are stronger already,” Clement told Sky Sports News HQ.
“We are trying to do business as early as we can so I can get my ideas across to those players before the start of the season. We’re not done yet and we are looking at doing some other things.
“Tom played very well whilst on loan here. He scored goals, was creative, and was very popular with the supporters. At the moment he is a Hull player but we would like to have him and the clubs are speaking.
“Jason is also another player who’s played here previously but is also with another club so it’s difficult to speak any further about that one.”
Clement is a highly-regarded coach after his pedigree with Chelsea’s academy and his three years as assistant manager to Carlo Ancelotti at Paris Saint-Germain and Real Madrid.
And he said: “Having worked with some of the best players in the world I can say that above all they are very professional.
“Almost without exception, the best players in the world are the hardest workers and we want that here.
“It’s not going to be easy but anything that’s worthwhile you have to work for. It’s a long season but we hope that with what we’ve got here we are going to challenge.”