With City not in action until a home game with Liverpool on Sunday, United can strike another psychological blow if they prevail at Craven Cottage.
Despite his side's struggle to beat Southampton, United captain Nemanja Vidic says the only thing that matters is putting points on the board.
United and Fulham met as recently as last weekend, with Vidic and his colleagues winning 4-1 in a one-sided FA Cup fourth-round encounter at Old Trafford.
Fulham secured only their second win in eight games by overcoming West Ham United 3-1 on Wednesday, moving them eight points clear of the relegation zone.
With Chelsea, Tottenham, Arsenal and Liverpool all dropping points in mid-week, Everton capitalised by winning 2-1 at home to West Bromwich Albion to close to within a point of the Champions League places.
As Spurs do not play until Sunday, when they visit West Brom, David Moyes' side will move into the top four if they overcome a floundering Aston Villa team that sank into the relegation zone last weekend.
Third-place Chelsea also recorded a 2-2 draw on Wednesday, although the context was quite different, as they conceded two late goals in a frustrating stalemate at relegation-threatened Reading.