The two tour operators are part of a seven-strong consortium that owns 42pc of the part-privatised National Air Traffic Services (Nats), but recently decided to go it alone and find a buyer for their holdings. Other members of the consortium, called the Airline Group, which includes Virgin Atlantic, British Airways, easyJet, Monarch Airlines and Lufthansa, are also considering a sale, said sources close to the situation.
Nats has been valued at about £1bn and the 12pc owned by Thomas Cook and TUI is understood to have attracted interest from pension funds and small infrastructure investors.
Private equity group 3i has also been linked to a potential purchase of the 12pc stake, which is expected to raise in the region of £120m to be shared between the two operators.
Peter Read, the chairman of the Airline Group, declined to comment on which airlines may offload their stakes.
A spokesman for Virgin Atlantic said: “Discussions continue between the members of the Airline Group to assess the possible options for a future sale.”
A spokesman for easyJet said it always viewed its stake in Nats as a “very long-term investment” and “that hasn’t changed”.
It is believed that BA will also maintain its position.
The ownership of Nats, which handles about 5,000 flights a day, has been under question for several years.
Last July, the Government abandoned a sale of its 49pc stake in the service after a two-year process.
Justine Greening, who was transport secretary at the time, said it was in the “best interests” of the taxpayer to retain a stake.