The League One side were a goal down at half-time in the fifth round against Nottingham Forest when Clough had discovered that a potential home clash with the Owls was next on the agenda.
The Blades came from behind to record a dramatic 3-1 win over Forest and could now meet their neighbours at Bramall Lane in the final eight if Stuart Gray’s side successfully navigate their postponed fixture with Charlton Athletic.
"Yes, we told them just before they went back out," he said.
"We thought 'what the hell?', we'll just tell them.
"I just said 'you've got 45 minutes, away you go. If we get the victory you might have a Sheffield derby yet'.
"A few of them didn't believe us actually so we just joked and said it was Brighton or Hull away.
"We had to come back and win the match so it might have been a small incentive for the players."
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