And she hopes some of those youngsters will follow in the footsteps of greatest ever Olympians – including her famous son Andy.
As well as inspiring young people to become more involved in sport, Judy says the Youth Olympics would help develop a new generation of coaches and volunteers.
Judy said: "Hosting the 2018 Youth Olympic Games would be a phenomenal inspiration for young people.
"There is nothing better than seeing other young people competing at the highest level."
Glasgow is facing competition from Buenos Aires, in Argentina, Guadalajara, in Mexico, Medellín, in Colombia and Rotterdam, in the Netherlands.
A key strength of Glasgow's bid is thought to be its world-class sporting infrastructure and investment in developing sport at a grassroots levels, including a recent partnership with the Lawn Tennis Association.
Judy added: "We really need public facilities for people who are inspired by what they see on television and want to go along and try the sport out.
"So it is great to see local tennis courts such as Knightswood Park and Drumchapel Park being resurrected."