Thomas Cook has set a deadline of May 7 for expressions of interest in its airline business, with Indigo Partners and Lufthansa among the likely bidders, sources said.
The heavily-indebted British travel group put its profitable airline business up for sale in February after profit warnings in 2018 left it needing to raise cash.
Thomas Cook's airlines business consists of Germany's Condor, as well as British, Scandinavian and Spanish operations.
A sale of the business, in whole or in part, would enable the world's oldest tour operator to invest more in its own hotels and improve its online sales.
A source familiar with the discussions said that Indigo and Germany's Lufthansa appeared most interested in the business.
Aer Lingus and British Airways owner IAG should not be ruled out and EasyJet has engaged in talks but is seen as less interested, the source added.
It is not clear whether Ryanair would bid.
Another source said that private equity groups KKR and Apollo might also look at taking over the whole of Thomas Cook.
The airlines business would provide access to valuable European slots linking Britain to Spain, Greece and Turkey.
Lufthansa executives have said repeatedly that the German airline wants to "play an active role" in consolidation.
Indigo, the private equity firm managed by Bill Franke, the veteran US low-cost airline investor, has previously made investments in several airlines including Hungary's Wizz.
Thomas Cook has been revamping different parts of its business this year, closing high street stores and reviewing its money division as it focuses on holidays.
The company was hit badly in 2018 when a hot European summer deterred customers from booking holidays through the year.
One banking source said the airline would fetch less than €1 billion. Thomas Cook has a current market value of just over €400m.
Sources said that competition issues could influence which parts of the business different suitors go for.
Sky News has said China's Fosun International, a Thomas Cook shareholder, was interested in its tour business.