Some of the most exciting and memorable moments in United's recent history have come in the competition, which United last won almost 100 years ago. In the build-up to the midweek clash with Championship side City, we revisited some of the best...
The original United
Until a remarkable 2-1 victory at Old Trafford last month, United had to go back to Valentine's Day in 1993 for their last victory over their namesakes from Manchester.
It came, of course, in the FA Cup, a fifth-round re-run of that season's opening fixture when Brian Deane made history with the Premier League's first goal in a 2-1 Blades win.
And the cup game went the same way, in front of just over 27,000 at Bramall Lane. A young Ryan Giggs put the visitors ahead on the half-hour mark, before Jamie Hoyland equalised minutes later.
Glyn Hodges put the Blades ahead five minutes before half-time and the Blades had an inkling it may be their day when Steve Bruce, later to become player-manager at Bramall Lane, missed a late penalty.
"Sir Alex Ferguson always liked us," Tommy Cowan, who played for the Blades that day, remembered, "because we were always a really together group. I think he saw comparisons between his side, who were always known for fighting right until the end, and ourselves in that regard. They were always coming at you, no matter what the situation was. We might not have had their ability, not all of us anyway, but we had that same attitude."
United went on to lose in the semi-final at Wembley that season.
Kelly the toast of Bramall Lane
There is just something extra-special about a big night game at Bramall Lane, under floodlights.
The atmosphere seems to crank up an extra notch, and more often than not United's players seem to respond.
March 17, 1998 was one such occasion. An FA Cup quarter-final against Coventry City went to a replay after a 1-1 draw in the first leg, and City looked to be going through thanks to Paul Telfer's 10th-minute strike.
But then David 'Reg' Holdsworth struck with a superb acrobatic effort in the 89th minute to take the game first to extra-time, and then to penalties.
There, Alan Kelly stepped up to prove United's hero, saving spot-kicks from Dion Dublin, David Burrows and Simon Howarth. Wayne Quinn hammered home the decisive penalty to send United into the semi-finals, and Kelly was chaired from the Lane pitch as a hero. Two fans tried to take off his boots, almost dislocating Kelly's ankles because they were tied on so tight.
To make it all the sweeter for a proud Irish international, the game was played on St Patrick's Day.
"I was in the mood for a celebratory drink after the match," Kelly added, "but that idea was a non-starter. All the pubs had shut so I couldn't get a pint! I ended up having a cup of tea instead and going to bed."
United looked like they were going to implode from within that season, especially when star striker pairing Jan Åage Fjørtoft and Brian Deane were both inexplicably sold and manager Nigel Spackman resigned.
But under caretaker manager Steve Thompson, a former Blades player, United reached the semis of the FA Cup, eventually losing to Newcastle at Old Trafford, and were knocked out of the play-offs by Sunderland.
Fear the beard
Few loan signings in recent memory have made as much impact on the club's supporters as John Brayford.
His subsequent full transfer didn't work out, wrecked by a bad knee injury, but after signing on loan from Cardiff City, Brayford helped propel the League One Blades to a remarkable FA Cup semi-final in 2013/14 with a deflected goal in the quarter-final against Charlton Athletic.
Ryan Flynn put United ahead against the Championship side, but it was Brayford's long-range strike that calmed the nerves and took United to Wembley.
"Wow, what a day," Brayford told SUFC Memories last year.
"I can hardly remember it to be honest. The atmosphere was incredible and the game was a blur – I can just remember coming out at the end in T-shirts that said ‘we’re going to Wembley’ and the Greasy Chip Butty song bursting out.
"The noise that day, the stadium was shaking – it really was incredible. I can hardly even remember the moment I scored, I got lost in the moment and it felt really surreal. Easily one of the best moments of my career."
It got better from there, too. Against another Premier League side in Hull City, United took a shock lead when Jose Baxter turned home Brayford's cross but were rocked when Yannick Sagbo equalised with three minutes to go in the first half.
Then United went ahead again, Stefan Scougall converting beautifully after Jamie Murphy's driven run.
League One United were 45 minutes away from an FA Cup final, and a place in the Europa League too.
"We came in at half time and everyone was silent, and we all just burst out laughing," Conor Coady, then on loan at United from Liverpool, remembered recently on the Super 6 podcast.
"If we'd have got to the final we'd have been in the Europa League and we were in League One. It was mental to even think of that so we just had a laugh to ourselves, and the game was incredible.
"We gave a great account of ourselves and the club is brilliant, I loved it there."
Sadly for United, it wasn't to be. Hull rallied in the second half and eventually triumphed 5-3 under the Wembley arch, with spontaneous applause ringing around the United end after Hull netted their fifth in injury time.