On Thursday, members of the city council's executive committee will be asked to agree the minimum pay level for staff should be increased from £7.50 an hour to £7.65.
The rise will benefit several hundred council workers but could increase the pay packets of more than 5000 in total.
The majority of those in line for rise will be women working in frontline care services who are employed by Cordia, the council's arm's length organisation.
It sets its own wage levels but it is likely it - and the council's other arm's length bodies - will follow the council's lead.
In 2009, Glasgow became the first council in Scotland to introduce what it called a Living Wage for its staff, prompting a number of other councils to follow suit.
Before the adoption of a nationally agreed award, the Glasgow Living Wage was the highest in the country.
The city council actively promoted payment of the Glasgow Living Wage among other employers in the city and about 150 organisations, with nearly 50,0000 staff, have signed up.
And in 2013/14 the Convention of Scottish Local Authorities adopted the Glasgow rate of £7.50 per hour as the figure for its national pay negotiations.
City council leader Gordon Matheson said: "If you are working then you should be able to afford to look after yourself and your family. Glasgow has led the way on tackling in-work poverty."
Brian Smith, Glasgow branch secretary for Unison, welcomed the increase in the minimum wage.
He said: "There will be hundreds of low-paid women who will benefit from this. We welcome anything that deals with some of the worst elements of low pay."