If I was a betting man I would think Easyjet, TUI, Wizz UK or a hotel chain could be contenders.
Easyjet operate from 2 sites at the airport with a car park off airport and run shuttle buses between the 3 sites. The Monarch building has a large car park which would be a bonus and would bring their buildings within walking distance of each other and could allow them to close their remote car park.
TUI are based a mile from the airport and also have to run bus services between their HQ, the airport and the station where one of their car parks is located. The Monarch building is a short walk from their airport operation and hangar.
Unlikely Wizz UK as I would think that would be run in the main from Hungary making the building too big.
Possible hotel conversion but it has been sold with no planning application to convert it. Whoever has bought it will have some sort of link to the airport.