The Chichester firm applied to Arun District Council to build 12.42ha of glass and provide new vehicle access by altering the alignment of Lower Bognor Road.
Reports say some local people have raised concerns that the development will cause traffic problems and would set a precedent for other large-scale developments in the area.
Brinkmans states the new facility is necessary because of the expansion of the business.
The planning documents submitted propose the glasshouses will replace existing agricultural land to the north east of Lagness, at Park Farm. Offices, a car park and a reservoir for storing rainwater will be built. The site would operate 24 hours a day, with 30 full-time staff and 20 part-timers employed.
The application states: "A new access road would be created across farmland south of the development site from Lower Bognor Road to the yard and car park. This new route would divert farm traffic within the farmland from an existing access road that is located in close proximity to Morrells Cottage, Park House and Park Farm Cottages to a new access road located away from the above residential properties among arable fields."
Brinkmans commercial director Paul Nicholls said he was not prepared to comment until further down the application process.