The Glasgow Academy, a fee-paying independent school, is holding an exhibition on Wednesday, June 22 to allow residents to view the proposals.
If approved by the council, the centre would replace the existing sports and music facilities with a multi-purpose hub.
External sports clubs and community groups would be invited to use the centre on an “ongoing basis”.
The event will allow attendees to learn about the plans, which include a swimming pool, indoor games hall and outdoor sports pitch.
There could also be “safe social” areas, flexible learning spaces, musical instrument practice rooms and quiet zones, with the school hoping to “enhance the creativity and well-being of pupils and visitors”.
Matthew Pearce, rector at the Glasgow Academy, said the school is “immensely proud of its sporting tradition, empowering children and offering the widest possible range of ways to stay physically and mentally healthy.
“We have a transformative opportunity to enhance the well-being of our pupils, today and long into the future.
“We are looking forward to sharing our vision that has been designed to create opportunities for our pupils and the wider West End community, that we already have a great relationship with.”
The community exhibition will take place between 4pm and 8pm on Wednesday, June 22 in the academy’s sports hall on Colebrooke Street.