Six carers, who would be affected by the planned closures of the Berryknowes, Summerston and Hinshaw Street centres, met with council leader Gordon Matheson, Councillor Matt Kerr and social work director David Williams.
Council bosses listened to the group's suggestions for a two-year delay on day-centre closures and the creation of a working group, which they said could help find alternative solutions.
Tommy Gorman, one of the campaign members, said: " We're putting across a very clear alternative to day-centre closures.
"We're taking into consideration an extended partnership model and a positive look at community cafes which could be used to provide work experience for people with learning disabilities.
"We have asked them to think and seriously reconsider the proposals as we're really concerned that there is a care crisis in Glasgow."
A Glasgow City Council spokesman said: "We cannot agree to a moratorium but we are sticking by our pledge that no-one will leave their day centre until their needs are fully assessed and alternative arrangements are in place."