The two teams are off from league duty as part of the winter break introduced this season.
But the Premier League would have allowed them to play the postponed game from the past weekend during the coming round of matches
Both clubs rejected the offer, per the Evening Standard.
It is unclear when the match will go ahead, given City are in the Carabao Cup final, still in the FA Cup and have Champions League duties as well.
City may be in a position of not having a midweek off after the winter break until they are eliminated from the FA Cup or Champions League later in the season.