The one for which planning permission was applied for in January 2015 and has not yet been granted. It is for 2500 spaces and for the replacement coaching facility. The existing coaching facility is I understand currently on what will be the site of the new multi storey car park mentioned in your post. The January planning application clearly states what it is for and is situate off Sunbank Lane and Wilmslow Old Road on the other side of the A538 to the logistics parks
An extract from the planning statement below
This Planning Statement has been prepared in support of an application for the development of land to the west of Wilmslow Old Road, south of Sunbank Lane and east of the A538 Wilmslow Road, Manchester for operational storage and car parking associated with Manchester Airport. The application seeks permission to develop the land to accommodate operational vehicle storage (bussing operartion and snow fleet) and long stay car storage (for up to 3,000 vehicles) that will be displaced by the development of Terminal facilities and new apron at the Airport. Additionally, it seeks permission for a realignment of Sunbank Lane to facilitate the development of World Logisitics Hub whilst preserving access to properties and businesses on Sunbank Lane and Wilmslow Old Road.