The League One club have seen off Aston Villa, Fulham and Nottingham Forest to reach the quarter-finals of the FA Cup, while the Addicks are defying their poor league form
Championship side Charlton Athletic stand in the way of Clough's League One outfit on Sunday and a place in the FA Cup semi-final.
United have already exceeded expectations to reach the quarter-finals by seeing off Premier League sides Aston Villa and Fulham, and then Clough's former club Nottingham Forest in the fifth round.
And having come so far, the former Derby County boss - named League One manager of the month on Friday - is determined to see his resurgent side go a step further and earn a trip to Wembley for a semi-final next month.
He said: "I don't think we would have dreamed with the draw we have had that we would be in the quarter-final.
"Somebody said the draw had been kind to us, but we have been away from home in the first three rounds, and then had Fulham and Forest.
"But to get to this stage as a League One club you're going to have to beat teams like that.
"I am just trying to get Sheffield United to Wembley because of what it will mean to everyone here.
"It should be in every player's mind, not to make them nervous, but they might never be this close to playing at Wembley again.
"I don't think we can win it because of the teams that are left in it, but if we get to a semi-final then anything can happen."
Clough has worked wonders since being appointed as David Weir's successor at Bramall Lane following his sacking by Derby, guiding United from the relegation zone to just outside the play-off pack as well as masterminding their impressive cup run.
The Yorkshire side have reeled off eight wins in a row in all competitions and not conceded a goal in their last five games.
That has led to the lowest-ranked side in the competition being billed as favourites to beat a Charlton side languishing in the Championship relegation zone, a notion that Clough has dismissed.
On-loan full-back Kieron Freeman is available to make his debut following his move from Derby this week, but Clough has doubts over John Brayford (calf), Jamie Murphy (groin) and Harry Maguire (knee).
Charlton were beaten 3-0 at Championship leaders Leicester City last weekend and will be bottom of the table if Yeovil Town and Barnsley win on Saturday.
A trip to Wembley would be a major tonic for boss Chris Powell, who is aiming to guide the London club to the last four of the famous competition for the first time since 1947 - when they went on to win the cup.
Charlton have doubts over Michael Morrison (thigh), Jordan Cousins and Simon Church (knocks), while Chris Solly and Leon Cort will play no part due to knee injuries.