No English club has ever won both the domestic cup competitions, the league and European Champions League in the same season but Abu Dhabi-owned City remain in the mix for all of them.
They are second in the Premier League, three points adrift of unheralded leaders Leicester City, and made sure of at least one trip to Wembley after beating Everton in the League Cup semi-finals.
They face Dynamo Kiev in the last 16 of the Champions League next month.
"It's not a target that we have in mind at the moment because it is not a realistic target," Pellegrini told reporters on Friday when asked about the quadruple. "We have to play against Aston Villa tomorrow. If we fail tomorrow, we finish talking about that."
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The Chilean said that fixture congestion could also become a problem, with the Feb. 28 League Cup final already forcing the rescheduling to a later date of a Premier League match against Newcastle United.
"If we continue in the FA Cup, if you want to arrive to the final we have at least two (Premier League) games more suspended so it's difficult if you continue in the Champions League to find a day where you can play all those games," he added.
Villa, bottom of the league, held City to a goalless draw in November and have started to turn things around with a run of five games unbeaten.
City meanwhile have a lengthening injury list with Belgian playmaker Kevin De Bruyne facing up to 10 weeks out with a medial ligament injury while Vincent Kompany, Aleksandar Kolarov, Eliaquim Mangala, Samir Nasri and Wilfried Bony are also unavailable.
Pellegrini said Bony was expected to be fit again in a couple of weeks while Kompany, Mangala and Kolarov could return to working with the squad next week.
The manager felt City had a big enough squad to cope, however, without the need for reinforcements before the transfer window closes on Monday.
"It is not our intention to bring in anyone in January. I trust in my squad and I am sure we will be competitive," he said.
(Reporting by Alan Baldwin, editing by Toby Davis)
