According to the plans, the former Ramarena Site was last used by Derby County more than 23 years ago.
It said the relocation of the cricket club would create “modern, high-quality” facilities.
“Relocating Alvaston and Boulton Cricket Club is essential to enable redevelopment of its current site as part of the Rolls-Royce Raynesway expansion.
“This wider scheme will deliver significant economic benefits such as job creation, supply-chain growth, and investment in a nationally important defence project,” plans added.