The Cardiff City loanee scored in the Blades' 2-0 victory over Charlton Athletic in the FA Cup quarter-finals earlier this month, but has not played since due to injuring his thigh.
However, the 26-year-old is close to full fitness and could feature against Wolverhampton Wanderers at Bramall Lane on Saturday.
"John would have played on Tuesday. That's the type of lad he is, but thankfully it's not his decision," Clough is quoted as saying by the Sheffield Telegraph. "Hopefully he could be back for the weekend."
Brayford has made nine appearances for United in all competitions since joining the League One club on loan in January.