The Premier League leaders restored their eight-point advantage at the top of the table over United on Sunday by coming from behind to beat West Ham 2-1 at home.
Second-half goals from Nicolas Otamendi and David Silva – the latter's volley on the end of Kevin De Bruyne's superb chipped pass coming seven minutes from time – overturned Angelo Ogbonna's opener and ensured City equalled Arsenal and Chelsea's Premier League record of 13 successive wins in the same season.
And now Delph wants Pep Guardiola's side to hold the record outright by taking three points off United, saying: "It'd be nice [to break the Premier League wins record at Old Trafford] because it's a derby.
"We want to win that game but we're taking it each game at a time. Hopefully we can get the three points in that game too."
13 - Manchester City have equalled the record for longest winning run in a single top-flight season, level with Sunderland, Preston (both 1891-92), Arsenal (2001-02) and Chelsea (2016-17). Rampage. pic.twitter.com/v921TYijYI— OptaJoe (@OptaJoe) December 3, 2017
Delph also praised City's patience after seeing off West Ham with their third 2-1 win in the space of a week.
It was difficult to level the same accusation convincingly against West Ham, who sat deep but had chances to lead through Michail Antonio and Manuel Lanzini before Ogbonna headed home Aaron Creswell's cross in the 44th minute, but England international Delph was frustrated by their approach all the same.
"I think the intensity was there but when you've got 11 men behind the ball it makes it difficult," he told Sky Sports.
"It's happened a few times this season. Teams seem to come here and get every man behind the ball, not interested in anything but parking the bus.
"But we have players like David in the team, so we knew if we kept going, kept plodding away, we'd get our chances.
"We knew we had to be patient. We came out flying in the second half, we tried to explain to the boys we still had time and then we started to relax a bit more and found those spaces."