Based on historical data Chelsea won Manchester united when they are on their home ground more than once and just like you stated Chelsea would do what they can to either maintain their Position or surpass Manchester city, this means that they need at least 3 points, I'm not entirely sure of this but Chelsea is the better side here...both teams have been rivals in the past but currently they are not on the same level when it comes to strength.
I'm not going to use past games to determine the results between both teams, as of now Chelsea and Manchester United are unarguably having a bad time, we can't even predict correctly who wins when they play, sometimes they play differently and win and after some game you can't accept the fact that either team are finding it difficult to beat a lesser team that was predicted on their favor.
Both teams will play and the result will be decided, Chelsea are not leaving their training ground for the match, so they should be very prepared to entertain Manchester United, if they lose against Manchester United their dreams of playing Champions League next season might be over.