The source said that IAG had secured the majority of the Monarch's slots at Gatwick Airport, which is Britain's second busiest airport.
The deal, first reported by Press Association, comes after Monarch won an appeal last Wednesday to have the right to sell airport slots for next year, a court ruling which was criticised by industry bodies such as the International Air Transport Association (IATA).
Monarch abruptly ceased operations in early October, leading to the repatriation of a hundred thousand customers by the British government.
EasyJet, Wizz and Norwegian had also expressed their interest in acquiring the slots at the London airports, while sources said that travel firm Thomas Cook had also bid for the Gatwick slots.
Monarch estimates its slots could be worth around 60 million pounds ($80 million) although that is disputed by airlines such as easyJet.
Monarch's administrators KPMG and IAG declined to comment.