The operation known as 'mixed mode' would allow Heathrow, already operating at capacity, to increase flights from 480 000 a year to 530 000. A record 70 million passengers used the London air hub in 2012.
Travelmole reports the airport responded to the publication of the Airports Commission consultation document on Thursday with a statement saying "it did not support the short term fix because it would increase noise pollution for nearby residents".
Instead, it insists the only way to solve the UK's shortage of hub capacity is by building a third runway.
The change in stance is seen as a tactical move by the airport to improve the chances of getting permission for an extra runway.
But in its consultation document, the Airports Commission suggested there could be more than one London hub, saying it was feasible for one of the three global airline alliances currently based at Heathrow to switch to another airport.