The £26m project includes the demolition and replacement of the existing south and east stands and the refurbishment of the stands on the north and west sides. This will increase capacity from 12,000 to 18,000.
Contractors have until 17 September to lodge initial requests to bid.
Windsor Park is home to Linfield FC as well as the national football stadium.
Project manager is Edmond Shipway, which is also looking after the redevelopment of Ravenhill Stadium in Belfast. This stadium is the Home of Ulster Rugby.