The 26-year-old linked up with the Blades on loan for the remainder of the season in January after failing to secure regular first-team football with his parent club.
When asked about keeping hold of Brayford and Conor Coady, who is on loan from Liverpool, Clough told the Sheffield Star: "In an ideal world we've love them to stay.
"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."
United sit 10th in League One, seven points adrift of the playoff places.