Three pilot schemes will start in the city to assess whether there is sufficient demand for a wider roll-out of the service.
Council leader Steven Purcell, who said the authority would work on the initiative with the voluntary sector, told Nursery World, 'One of the biggest obstacles that people face in getting into or staying in work is finding good-quality, affordable childcare.
'It makes sense that we work with various childcare providers to expand the provision available in Glasgow to give working parents more options.'
Sue Robertson, director of One Parent Families Scotland, which runs an out-of-hours childcare service in association with Stepping Stones in Glasgow, said, 'We welcome any recognition in principle that childcare needs to extend beyond normal hours, but I believe it would be important that any new developments are linked to existing services.'
One Parent Families' 'sitter' service, which involves childcare in the family home, runs from 6.30am to midnight, seven days a week. It costs up to 17 an hour, with a sliding scale of charges based on income.
Services receive funding from the Working for Families programme, which helps people from disadvantaged areas into work.
Ms Robertson said her organisation would like to be involved in the plans, but warned that provision during unsocial hours was expensive and the council would need to ensure it was properly funded. She added that it would make economic sense if the provision was group-based.
Bronwen Cohen, chief executive of Children in Scotland, also welcomed the council's plans, which she said reflected 'the reality of modern families'
lives'.