Boris Johnson, the mayor of London, and international development secretary Justine Greening are set to fight expansion, The Sunday Telegraph reported.
However, 30 MPs are believed to have signed a letter calling for David Cameron to “push ahead” with a third runway.
An announcement by the primer minister is expected over the coming days.
In July the Airports Commission led by Sir Howard Davies recommended expansion at Heathrow – but left a possible second runway at Gatwick on the table.