The new pavilion would be installed, subject to planning approval, at the historic Ufford Park, off Ufford Hall.
Mr Agnew previously played for Ufford Park Cricket Club before going onto represent Leicestershire and England. He has since enjoyed a long and successful post-playing career as a broadcaster on Test Match Special.
His bowling run-up was once described as being so long that he could barely fit it into the ground.
The application for the new pavilion, which has been submitted to Peterborough City Council, states: “It is proposed to demolish the existing modern brick cricket pavilion, together with the timber structure immediately to its north, keeping the scoring hut and replacing these two structures with a single entity.
“This proposal is driven by two goals – firstly, to provide a better facility for a thriving cricket club and secondly, to provide a more aesthetically pleasing pavilion sitting on the edge of the historic park off Ufford Hall.
“The park is a locally registered asset and the current pavilion does not sit comfortably within that environment.”
It adds: “The new proposal is a better design, more than complies with minimum standards for changing rooms and will provide a much better facility for both the club cricketers and their associated social events.”