The Glasgow Connectivity Commission recommended creating a city-wide tram network as part of its plan for a 21st-Century sustainable transport system.
The proposal is to build a line from Glasgow Airport to Paisley Gilmour Street train station and then extend it to Glasgow city centre.
Funding for a link from Paisley to Glasgow airport has been approved by Glasgow and Renfrewshire councils and a feasibility study is to be carried out to extend it eastwards to Glasgow.
Scottish Government approval for it to be a national transport project is needed but consideration of a metro system has been included in the Programme for Government.
Both council leaderships are now in agreement and approval of the full councils will be sought for what will be the biggest public transport project in the city for decades.
Susan Aitken, leader of Glasgow City Council, will give an update on the plans at the State of the City Economy conference this Friday in Glasgow.
Ms Aitken said: "It's less than a year since the expert Connectivity Commission proposed a Glasgow metro but already our ambitions are making considerable progress.
"The Scottish Government has pledged to work with us on the Commission's recommendations, while Glasgow and Renfrewshire councils will undertake the feasibility work required to ensure it can be considered as a key, national project.
"Funding is already in place to deliver a first phase linking Paisley with Glasgow Airport."
She said it made sense for the airport link to be the first phase in a city-wide network.
Ms Aitken added: "We need to improve how our people get around if Glasgow is to build on its potential as a global city.
"For these reasons and more, the case for a Glasgow metro is compelling."
A section of the Scottish Government's Programme for Government states: "We are committed to working with partners to consider the Commission's recommendations and, as part of the second Strategic Transport Projects Review, we will consider the potential for a Glasgow Metro, which builds on the planned City Region Deal investment to link Glasgow Airport and the new National Manufacturing Institute for Scotland to Paisley Gilmour Street."
Glasgow City Council is working with Renfrewshire Council to deliver the airport link as part of the £1.1 billion City Deal.
It is hoped the metro plan will finally provide a solution to the lack of an alternative to the M8 motorway for accessing the airport.
Mark Johnston, managing director of Glasgow Airport, said: "The city's metro proposals are compelling and demonstrate real ambition to deliver a much-needed, sustainable transport system.
"In particular, we welcome the commitment to deliver the airport corridor first and the Scottish Government's support for the project.
"This will have a transformative effect on the major employment sites along this route, alleviating congestion, reducing emissions and boosting public transport use."
A spokeswoman for Renfrewshire Council, said: "A public transport link from Paisley Gilmour Street to Glasgow Airport is critical to improving sustainable travel choices and will make a significant impact on improved journey times and connections for business and for airport users and employees, reducing the impact of traffic on the M8 at a key corridor and supporting thousands of new jobs."