The West Didsbury-based club wants to build a new state-of-the art facility at its Palatine Road site, which would feature an environmentally-friendly green roof.
Under the scheme, the Northern Lawn Tennis Club hopes to replace an existing red brick building, housing one indoor double tennis court, with a larger building and external landscaping.
The existing building is 11.5m high but the proposed development would see the new building sunk 1m into the ground.
The development would also include landscaping of the area around the building.
The development uses a green roof system, lining the roof with a layer of sedum plants. The system uses year-round flowering plants, which attract wildlife and provide food for insects and butterflies. It also aims to absorb carbon dioxide, improve air quality and produce oxygen.
The application will be heard on 12 February by Manchester City Council.