Attention will now switch the clash of the arch-rivals and title contenders at Etihad Stadium, when local pride and top spot in the Premier League will be at stake.
But before the sides meet, both have relatively minor Champions League business to take care of.
United face Cluj in a dead rubber while City, already eliminated from the competition, travel to Borussia Dortmund looking to secure a consolation spot in the Europa League.
Hart said: "We move on to the derby now, and we've obviously got Dortmund on Tuesday.
"We've got a tough one in Dortmund. We need to finish the Champions League group with a bit of pride.
"Hopefully we'll get a good result there and we'll get into that one (derby). We'll deal with that when it comes."
City trail United by three points heading into the derby but remain unbeaten after a hard-fought 1-1 draw with Everton at Eastlands.
The champions needed to come from behind after Marouane Fellaini turned in a deflected Leighton Baines cross at the second attempt after 33 minutes.
Their equaliser came from a controversial penalty before the break after Fellaini was adjudged to have fouled Edin Dzeko at a corner.
It was a soft award and led to protests from Everton but Carlos Tevez made no mistake from the spot.
Hart saved well from a Fellaini header and a Nikica Jelavic free-kick in the final moments of each half but City generally dominated the second period.
The result extended City's unbeaten home run in the Premier League to 37 games.
Hart said: "It's a great record - one we need to keep going, but with more wins than draws.
"It was a tough game. It is always going to be tough against Everton. We'd like to win but we haven't lost.
"They are a good team, they work for each other. They have got some good players and a good manager, and all that added together makes them a tough team to play against."
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