The Walney wind farm, off Barrow, already has 102 turbines and generates enough power for about 320,000 homes.
Danish-based developer Dong Energy wants to add up to 120 additional turbines and provide power for about 500,000 more homes.
If the Planning Inspectorate approves the project, work on the new turbines could be completed by 2017.
When it was officially opened in February 2012, Walney was the largest offshore wind farm in the world.
It was built in two phases with the second set of 51 turbines completed in six months - a record for the wind farm sector.
If approved, the extended wind farm will cover an area of about 57 sq miles (149 sq km).
Plans which could see a wind farm off the Cumbrian coast more than double in size are to be submitted.