City -- who have a historic quadruple in their sights -- Chelsea and Spurs are strong favourites to reach the last eight as they face lower league opposition.
Jose Mourinho's United travel to Huddersfield, where they were beaten earlier in the season, desperately seeking to rekindle their form after a shock defeat at Newcastle.
Chelsea's defining month
Hull City's visit to Stamford Bridge on Friday may be the calm before the storm for Chelsea, coming ahead of a "massive" few weeks for the English champions, according to manager Antonio Conte.
The pressure on the Italian was eased by a routine 3-0 win over West Brom on Monday, which took Chelsea back into the top four ahead of daunting visits to United and City in their next two league outings.
Either side of their trips north, Chelsea face Barcelona in a two-legged blockbuster Champions League last-16 tie.
Conte has welcomed the return to fitness of new signing Olivier Giroud and Alvaro Morata to give him options up front, with both set to feature at some stage against Hull to get them up to speed ahead of Barca's visit to London on Tuesday.
Wigan and City worlds apart
A lot can change in five years. The greatest moment in Wigan's history came in 2013 when they shocked Manchester City 1-0 at Wembley to win the FA Cup.
Since then the fortunes of both clubs have radically diverged. Wigan have suffered three relegations in five seasons, while City travel to Wigan on Monday aiming to continue their relentless march in four competitions.
Pep Guardiola's men all but guaranteed their place in the Champions League quarter-finals with a 4-0 thrashing of Basel in midweek to go with a 16-point lead at the top of the Premier League and a place in the League Cup final against Arsenal next weekend.
From Champions League to Spotland
Tottenham's rise under Mauricio Pochettino shows no sign of abating after they came from 2-0 down inside 10 minutes to draw 2-2 at Italian champions Juventus with a hugely impressive performance in the Champions League on Tuesday.
But a very different peril awaits on Sunday when they travel to Rochdale to play on a surface Pochettino has described as "not a pitch in a condition to play football".
Rochdale promised to relay the turf after last weekend's game against Fleetwood was called off due to a waterlogged pitch.
Concerns over the surface could also provoke Pochettino to name a much-changed side, particularly after an energy-sapping four-game run against United, Liverpool, Arsenal and Juventus.
How to solve a problem like Pogba?
He may have cost United a then world record £89 million ($125 million) in 2016 but Paul Pogba has recently been the fall guy as Mourinho struggles to piece together a side that gets the best out of the Frenchman and January recruit Alexis Sanchez.
Pogba and Sanchez are yet to complete 90 minutes together since the Chilean's switch from Arsenal, as Pogba has been hauled off by Mourinho in defeats at Spurs and Newcastle and dropped for Sanchez's goalscoring Old Trafford debut against Huddersfield.
"It's very difficult to put me in a position where I have to criticise my players," said Mourinho when quizzed on Pogba's lack of form.
Another meeting with Huddersfield on Saturday gives Mourinho the chance to find a balance in attack before a testing run of fixtures that includes Sevilla in the Champions League and the visits of Chelsea and Liverpool in the Premier League.
Fixtures (all times GMT)
Leicester City v Sheffield United (1945)
Chelsea v Hull City (2000)
Sheffield Wednesday v Swansea City (1230), Brighton v Coventry, West Brom v Southampton (1500), Huddersfield v Man Utd (1730)
Rochdale v Tottenham (1600)
Wigan v Manchester City (1955)