The proposed facility is to be built at the southern end of the school's Chorley New Road campus, adding to its existing sports amenities.
If given the green light, the new development will feature a 722 square metre dome with retractable sides to provide flexibility.
A connecting pavilion will be built for classroom teaching and storage.
Proposed indoor dome will expand Bolton School's sports capacity for tennis, basketball, badminton, and netball across all student age groups (Image: Bolton School)
Philip Britton MBE, Head of Foundation, said: "The development of additional indoor sports facilities for the use of students across the Foundation has long been a priority for the Governing Body.
"Should this planning application be approved, the sports dome will add much-needed capacity for curriculum teaching and extra-curricular activities in tennis, basketball, badminton and netball, which will benefit students from the Primary Division through to Sixth Form.
"During the past year, the School has received two hugely generous legacies from Old Boys who wished to support the development of our sports facilities for the next generation of pupils."
Mr Britton added: "Their generosity has made it possible for the School to begin this exciting project, as we continue to ensure Bolton School remains both affordable, and worth affording, for the families in our community."
CopriSystems will design and construct the custom indoor sports dome for Bolton School, pending approval from Bolton Council (Image: Bolton School)
The construction of the new sports dome will not interfere with the existing First XI cricket pitch and pavilion.
The school's new partner in this project is CopriSystems, a company that specialises in the design and construction of customised sports facilities.
The school said it plans to complete the construction by August 2027, in time for the 2027-28 academic year, subject to planning approval.