Glasgow is up against Buenos Aires in Argentina and Medellin in Colombia, for the event, with the final decision to be announced in July.
Speaking at Shawland's Academy, Lord Coe said Glasgow had a "unique opportunity" to build on the success of London 2012 with next year's Commonwealth Games and that the Youth Olympics would enable children to share cultures, respect differences and be inspired by sport.
Shawlands Academy, where pupils speak more than 50 languages, was recently handed the International School Award by the British Council, based on its twinning and e-twinning projects with countries around the world.
The school has been at the centre of the Youth Olympics bid, with pupils taking part in a consultation about Glasgow's candidature file.
Lord Coe, who was joined on his visit by Common-wealth Games and Sport Minister Shona Robison and Glasgow City Council leader Gordon Matheson, said: "Every sporting event that matters is happening on our shoreline. To go from the Olympics to the Common-wealth Games and the World Athletic Championships – there is not a nation that can boast that.
"Sport is the most proactive social worker in the world. It changes people's attitudes."
Lizzy Pollard, 15, a fourth-year pupil at Shawlands and student champion for the Commonwealth Games, said: "We already have the facilities we'll need to host the Youth Olympics. And we are a friendly city and will be able to welcome the people who come here to watch it."