Brayford and Coady are set to see out the season at Bramall Lane after joining the Blades from Cardiff City and Liverpool respectively.
Clough admits it will be ‘difficult’ to convince the pair to step down from Premier League employers and remain in League One, but he will be doing his best to talk them round.
“In an ideal world we’ve love them to stay,” he told the Sheffield Star.
“For a number of different factors, we probably wouldn’t be looking at permanents but, you never know, there might be a chance of securing similar agreements again.
“Both clubs have done us a big favour by letting us get them on the type of deals we have. And, quite rightly, they are the ones who are going to have the final say on all of this.”
Clough is also holding talks with former employers Derby County about the prospect of keeping Freeman on his books, with the defender’s initial loan agreement set to expire following Saturday’s home date with Leyton Orient.
He added: “We’ll be trying to keep Kieron until the end and that conversation has already started.
“He’s versatile and there are very few who can operate as comfortably as he can at either left or right-back.”