The city council's pension fund - the Strathclyde Pension Fund - is part of a bid consortium which includes Partners Group and Zurich Airport.
Partners Group is a global private markets investment management firm with more than €30 billion in investment programmes under management in private equity, private debt, private real estate and private infrastructure.
It is understood Spanish firm Ferrovial is also keen on snapping up Glasgow. It presently owns London Heathrow Airport as well as 25% of Heathrow Airport Holdings which owns Glasgow, Aberdeen and Southampton Airports.
A decision by the Strathclyde Pension Fund group to also try to buy Glasgow could spark a bidding war.
Insiders say the consortium regard the west of Scotland airport as a good investment.
And the source said the move to buy Glasgow is supported by city council leader Gordon Matheson and Renfrewshire council leader Mark Macmillan.
They regard the airport as a vitally important asset to the West of Scotland in general but to Glasgow and Renfrewshire in particular.
Strathclyde Pension Fund has assets of £13.5bn making it the wealthiest council pension fund in the UK. Its members include the 12 local authorities which made up the former Strathclyde Regional Council.
However, the fund has around 200,000 members including present and former council staff and a number of private companies such as bus giant First.
The pension fund has spread its investments across a wide range of areas and has a stake in some of the biggest companies in the world, including Samsung and Apple.
It also has a property portfolio which includes a Wolverhampton shopping centre and an office block in Hong Kong.
Glasgow Airport was owned by the former Glasgow Corporation but in 1975 an agreement was reached to transfer its ownership to the British Airports Authority.
Manchester Airport is one of only a few airports in the UK still in the ownership of local councils.
It is owned and managed by Manchester Airports Group, a holding company owned by the 10 metropolitan councils of Greater Manchester.
Last year, the consortium decided to buy Stansted Airport and 35.5% of the group went to Australian investment fund Industry Funds Management.
In the battle to win the bid, pension fund managers face a major fight to wrestle control of the west-coast hub.
They could be caught up in a bidding war after Madrid-based Ferrovial reportedly tabled an opening offer of £800 million earlier this week for Glasgow and the airports at Aberdeen and Southampton.
Ferrovial is the world's largest transportation infrastructure company and is cash rich. Technically, it already owns Glasgow which is part of Heathrow Airport Holdings (HAH) which also owns the other two airports. The Spaniards have a 25% stake in HAH and is its biggest single shareholder. But it's looking to expand business interests in the UK and reports suggest it wants outright control of Glasgow Airport and the others. It already has full control of London Heathrow.
Ferrovial took control of what was BAA in June, 2006, at a time when officials in Glasgow were celebrating the west coast hub's 40th anniversary.
The Spanish conglomerate has so far refused to comment on reports of a bid although sources insist the speculation is true.