But it has called on the city council to listen to the concerns of people affected by the move.
The council is consulting on plans to close centres at Berryknowes, Summerston and Hinshaw Street, at Queen's Cross, which accommodate about 130 people each weekday.
Social work bosses say some of the centres are in poor condition and offer limited services.
They say reforming how the service operates would provide more opportunity for people in mainstream centres, would allow them to get involved in other activities and would also save money.
The move has been backed by Jo Armstrong, chairwoman of learning disability charity Enable Scotland.
She said: "We welcome the modernisation, but we call on the council to ensure those affected are listened to, understood and reassured that the alternatives made available to the 320 people continue to deliver the outcomes people value so highly."
Anne MacKinnon, chairwoman of Enable Glasgow, said: "We would call on Glasgow City Council to ensure anyone affected by changes to day service provision has a full assessment and is offered an appropriate alternative service before they lose the day centre place they have depended upon.
"Failure to do so is likely to result in isolation, distress and, ultimately, to additional demand on services elsewhere in the sector.
"Many of the people who will be affected if Glasgow City Council proceeds with its plans will be older family carers and their sons and daughters who live in the family home. We know this group are often particularly dependent on services and so will be especially anxious about the proposed changes."
Matt Kerr, the council's spokesman for social work, insisted the council would listen to the views of everyone involved.
He accepted the change would be worrying for some people but added: "We are not in the business of closing centres without replacement services being made available.
"That would be a disaster and that is why we are not going down that route. Nothing will close without alternatives being available.
"The consultation finishes at the end of January but this will be a long- running process as it could take over 12 months to get everyone's needs properly assessed.
"Services will be in place before we think of closing anything."