The city - which has put events at the heart of its tourism strategy - hopes to follow this summer's showcase with a series of small competitions in individual sports.
But sources have confirmed it has looked at a specific bid for the new European Games, to be held for the first time next year in Baku, Azerbaijan.
Glasgow was in early contact with the European Olympic Committee about staging the Games as early as 2019, The Herald can reveal, but is now understood to be thinking about a later bid.
A spokesman for Glasgow City Council said: "Glasgow is not a candidate city for 2019."
But he added: "The European Games are an exciting addition to the world's elite sporting calendar and one that Glasgow may well bid for in the future."
Europe was the last continent to plan its own version of the Olympics after the Asian Games, which date back to the 1950s and are the second biggest multi-event sporting tournament in the world.
A European Games bid from Glasgow would reflect an ambitious step up even from the Commonwealths. Baku's debut European Games will feature 19 sports over 17 days, compared with 17 sports over 11 days at the Commonwealths.
Unlike the smaller, single-sport championships for which Glasgow is bidding, hosting the European Games would mean building another athletes' village - as the Commonwealth Games one in Dalmarnock will be turned in to housing when teams move out.
Such a village, moreover, would have to be relatively close to the new facilities, such as the purpose-built Chris Hoy velodrome near Celtic Park. Finding and decontaminating a site in Glasgow's historic industrial heart would need a huge effort but insiders argue it would bring rewards.
Glasgow tried and failed to win another Olympic event, the 2018 Youth Olympic Games, with an athletes' village proposed for Sighthill. The development, however, will go ahead, as a legacy of the bid rather than the Games, which will be held in Buenos Aires.
The council spokesman said: "As we have seen at the Commonwealth Games athletes' village and in the Sighthill regeneration, this sort of event gives a city a great opportunity to decontaminate unused land and turn it into a new neighbourhood."
Several other major cities were understood to have signalled an interest in the 2019 games, including Amsterdam and Istanbul, which have both been bidders for recent Olympic Games, and the Russian resort of Sochi, which hosted this year's Winter Olympics.
Oil-rich Baku also fancies itself as a future Olympic host city.
Glasgow has no such ambitions.
A source said: "The Olympics are for mega-cities but Glasgow's 2014 legacy may just be that a city-region of around one million can successfully host an event the size of the Commonwealth Games."