CrossReach wants to start the project at Doges, overlooking Glasgow Green.
Threshold Glasgow, part of CrossReach - the social care arm of the Church of Scotland - says its service, which supports adults with learning disabilities, autism and mental health issues, is seeing an increase in users.
To help manage this, and to ensure activities are socially distanced, the group wants to take over a unit inside Doges, which sits between two units it already uses.
What is Threshold Glasgow?
The organisation supports around 100 people in Glasgow - some at their home, some at community facilities, and others who use the Day Opportunities service.
This service, which gives its users the chance to learn and develop, has seen a big increase in users.
The new unit, if approved, would allow the group to run sessions including yoga, arts and crafts, and educational activities.