Deputy First Minister Nicola Sturgeon said the proposed changes highlighted the SNP administration's "commitment to doing as much as possible to tackle pay inequality".
She revealed the Scottish Government wants to amend the Procurement Reform (Scotland) Bill going through Holyrood.
But Labour have demanded ministers go further, and make it mandatory that all firms who are awarded public sector contracts pay their staff the Living Wage.
Labour MSP James Kelly said: "This is a chance to send out a powerful signal in support of fairness, it's time for Parliament to stand up for working people and it's time for the SNP Government to stand up and be counted."
Ms Sturgeon said the Scottish Government would put forward amendments to the Bill so that public authorities would be required to set out in their procurement strategies what their policy is in relation to ensuring companies they give contracts to pay the Living Wage.
The Bill will also allow ministers to issue statutory guidance on workforce matters - including pay - for the procurement process. An amendment proposed by the Government would include an explicit reference to the Living Wage in the Bill, and make it clear it is one of the factors authorities must evaluate, where relevant.