The move could spend the end of the legislation in its current form as the minority SNP Government is dependent on the support of the Greens.
Scottish Greens Cllr Anthony Caroll said: "As this Bill stands it is clearly not fit for purpose and we cannot support it.
"There is real concern from councillors across the country that the National Care Service as proposed will take away local accountability of social care and leave that in the hands of Scottish ministers.
Scottish Greens MSP, Gillian Mackay, said: ‘The proposed Bill is far from what we want it to be and, its present form, we can't support it.'
Mackay said the Greens wanted to see the scope of the legislation ‘radically reduced' to focus on ‘increasing support and rights to those providing care, including unpaid carers'.
The Bill has already lost the support of Scottish councils and unions.
Speaking earlier this month, Scottish Trade Union Centre general secretary Roz Foyer said the Bill ‘fails to address fundamental issues about how social care is delivered and has lost the confidence of workers in the sector'.