The 173-year-old business is battling to return to profit, and under Green’s tenure has more than halved losses in the past financial year.
The chief executive outlined plans for a further wave of cost reductions in November at the time of the group’s full-year results. It has already slashed its network of travel agencies from more than 1,100 to fewer than 900, with the loss of some 2,500 posts.
While Green has not ruled out further job cuts, she has stressed that the focus of the plan lies with other areas of the business.
Numis analyst Wyn Ellis expects the group to have narrowed underlying losses in its first quarter from £70 million for the same period a year earlier, in what is traditionally its weakest three months. However, unrest in Egypt and Thailand is predicted to have had some negative effect.
He added: “We believe that the poor weather in the UK over the last several weeks may have helped to stimulate early summer booking.”
Credit Suisse analysts described Thomas Cook as a “compelling turnaround story”.
The figures will come days after an update from rival TUI Travel noted that summer 2014 bookings in January had seen higher average selling prices and volumes.