The Glasgow SNP group says it will protect the centres using money redirected from the failed George Square redevelopment, but the city's Labour group is thought to be looking for its own alternatives.
The council announced in November that it wished to close the centres, arguing that users would be better served by more personalised services.
However, carers and service users have been vocal in opposition to the plans and last month the council's own Carer's Champion, Dr Christopher Mason, warned that consultation on the plans had been insufficient and called for a decision to be postponed and proposed a city wide review of learning disability services.
Ahead of the city's budget meeting on Thursday, Glasgow SNP social work spokeswoman councillor Susan Aitken said funds had been indentified to support the most vulnerable people in the city.
She said: "We have found resources to renovate our learning disability day care centres. We will do this by redirecting capital resources earmarked for the failed George Square redevelopment."
She said the alternative budget would allow for a full consultation with users and carers and claimed it would allow it to reverse the introduction of charges for community alarms.
The Herald understands there is mounting opposition to the closure plans among Labour councillors which could see a U-turn, with meetings held recently about how the administration can potentially avoid a closure decision.
Senior sources have said the political head of social work, councillor Matt Kerr, has been taking soundings from colleagues.
One possible get-out is to kick the plans into the long grass by agreeing to Mr Mason's recommendations.
The weakened position of the council leader Gordon Matheson, after revelations about his private life and his role in the fiasco around the cancellation of a competition to redesign George Square has also led to pressure for the centres to be given a reprieve.