In a letter to council leader Gordon Matheson, Mr Neil proposed to fund a study into alternative care options for people with learning disabilities - as long as Mr Matheson agreed to a moratorium.
Mr Neil wrote: "I offered to write to you to express my concern at the carers' situation and to suggest we consider together what more might be done.
"In the event you agree to a feasibility study, the Scottish Government would be willing to consider contributing to the cost of this provided you agree to a moratorium."
Tommy Gorman, a member of a campaign group fighting to stop the closure of the centres in Summerston, Berryknowes and Hinshaw Street, Maryhill, said: "I think it would be very irresponsible of the council not to take up this opportunity so it can at least determine what is the extent of the support being offered by Alex Neil."
However, speaking in place of Councillor Matheson, Malcolm Cunning, the council's spokesman for social care, described the letter as "nothing more than political posturing by the Scottish Government".
The council previously rejected the requests to stop the closures, and suggested giving the families affected personal budgets to pay for their own care needs.
As previously reported in the Evening Times, a total of 320 people with learning disabilities will lose day centre places under the plans to close the three centres.
About 200 adults with severe learning difficulties, many also with physical disabilities, will continue to attend council-run centres at Riddrie, Calton, The Wedge and Southbrae.
But the 320 will no longer have access to the day centres, which many have attended for years.
A Scottish Government spokesman said: "Local authorities must listen to and engage with all individuals affected by those decisions.
"That is why the Health Secret-ary has written to Gordon Matheson offering for the Scottish Government to contribute to the costs of the study into alternatives to day centre closures, so we can work together with Glasgow City Council to ensure sufficient time and space is provided for people to influence these crucial decisions that affect their lives."
However, Councillor Cunning said: "Ministers have already indicated their support for our proposed way forward and have provided funding to third sector partners to help deliver this.
"In addition, they have previously promised us money for a feasibility study on another issue, but this has never been given. So this letter appears to be nothing other than political posturing by the Scottish Government.
"Day centre closures is a very emotive issue in Glasgow and I believe carers deserve better than that from ministers."