Charity Horizon Leisure Centres wants to make the huge investment at its Waterlooville site after the success of an extension in 2015.
If the bid is approved by Havant Borough Council, a new car park would be built on site at Waterberry Drive and the centre would be extended again to provide additional leisure activities.
The new plans include greater provision for disabled parking and improved access to the centre for pedestrians and cyclists, with a new and enlarged covered cycle store.
The activities to be included have not been revealed due to commercial sensitivities.
The move comes as the charity’s chief executive, Howard Broad, said the population in the area is set to increase because of housing developments.
Mr Broad said: ‘The charity is delighted to start the process of providing more quality leisure facilities so desperately needed by the increasing demands, and the additional population of the area.
‘The provision of new locally accessible and affordable sporting facilities is essential for community wellbeing.
‘We’ve been overwhelmed by the feedback from our last extension. We must re-configure the existing car park and get a single-deck one built to meet current needs.
‘As far as the building extension is concerned, that would take place within 18 months to two years.’
Property firm Grainger PLC will provide £1m of the funding as part of its development to the west of Waterlooville.
Councillor Paul Buckley, who represents Waterloo ward, said: ‘It’s great news Horizon is looking to progress the second phase of its Waterlooville expansion. I was instrumental in ensuring Grainger’s money was directed for use in this way.
‘I’m keen for the project to include a sports hall to support indoor games such as badminton, basketball, or five-a-side football.
‘This expansion should coordinate with the council’s policy for development of leisure facilities across the borough and I will be monitoring this closely. I want Horizon to provide the facilities all residents of Waterlooville need and I hope there will be a public consultation on the application in due course.’
In 2015, a split-level gym, children’s indoor soft play area, cafe and more parking was added at the centre.