City, three points clear at the top of the table, travel to Everton while second-placed champions United are at home to Stoke.
Table-toppers City will again be without striker Mario Balotelli as the forward continues his four-game ban for stamping on Tottenham's Scott Parker.
"I do not agree with this decision, but we can do nothing," said City manager Roberto Mancini. "I explained to Mario and he understood."
City have only managed one victory at Goodison Park since 1992 but Everton, hampered by injuries, are set to be without first-choice central defenders Phil Jagielka and Sylvain Distin, along with Leon Osman, Jack Rodwell and Seamus Coleman.
United goalkeeper David de Gea struggled with crosses and corners in the 2-1 loss to Liverpool and Stoke, renowned for their physical presence at setpieces, are sure to test the Spaniard.
But United manager Sir Alex Ferguson tried to shield de Gea from criticism after the Liverpool match by saying: "Our own players created a problem for the first goal They didn't give him enough room to deal with it."
Third-placed Tottenham Hotspur, despite manager Harry Redknapp spending much of last week in court on tax evasion charges, still got through to the last 16 of the FA Cup after beating Watford.
Tuesday sees Spurs, eight points behind City, look to stay in the title race at home to bottom of the table Wigan.
The transfer window also closes on Tuesday but Redknapp said he did not expect to add to his impressive squad before the deadline is up.
"I can't see an awful lot (happening)," said Redknapp.
Legal action of a different kind will also be on the minds of many Chelsea fans when their side travels to Wigan on Tuesday -- just a day before skipper John Terry is due to appear in court on charges of racially abusing QPR's Anton Ferdinand -- an allegation the England captain denies.
Both Terry and Ferdinand were involved in Chelsea's 1-0 FA Cup win over QPR on Saturday -- the first time the two players had faced each other since the allegations surfaced.
On the field, fourth-placed Chelsea will want to strengthen their grip on a Champions League place against a promoted Swansea side who have been one of the success stories of this Premier League season so far.
"It's important to try and reach the top and go to Swansea fully motivated," said Chelsea manager Andre Villas-Boas.
Liverpool, five points behind Chelsea, may be in one Wembley final (the League Cup) and closing in on another, but forcing their way into the top four remains a key ambition for the Merseysiders ahead of their trip to second-bottom Wolves on Tuesday.
Their cup wins came after a dispiriting league defeat by lowly Bolton and Liverpool striker Dirk Kuyt, who scored the winner against United, said: "Everyone was really disappointed about the Bolton game.
"We have proved many times we can compete with the best teams. Now it's really important to play well against the other teams. That starts with a very important game against Wolves on Tuesday."
Wednesday sees Arsenal, who knocked Aston Villa out of the FA Cup after coming from 2-0 behind to win 3-2, up against Bolton.
"I hope it will convince the team we have the qualities needed and we can transfer that to the Premier League," said Arsenal manager Arsene Wenger.
Villa and QPR will look for league consolation after FA Cup exits when they face each other on Wednesday, with strugglers Blackburn facing giantkilling victims Newcastle, Fulham playing West Brom and Sunderland at home to Norwich.
Fixtures (1945GMT unless stated)
Tuesday: Everton v Manchester City (2000GMT), Manchester United v Stoke (2000GMT), Swansea v Chelsea, Tottenham v Wigan, Wolves v Liverpool
Wednesday: Aston Villa v QPR, Blackburn v Newcastle (2000GMT), Bolton v Arsenal (2000GMT), Fulham v West Brom (2000GMT), Sunderland v Norwich (2000GMT)