Ross Doyle, 17, was taken on as a trainee mechanic at In-Tune Garage Service in Maryhill five weeks ago.
Bosses say his potential is "immense".
However, the teenager has been turned down for the Commonwealth Apprenticeship Initiative because he was schooled in Bearsden, outside the Glasgow City boundary.
Apprentices must be educated in Glasgow to qualify for the scheme, organised to provide a legacy from the 2014 Games.
The garage previously took on another school leaver under the scheme, who went on to win Apprentice of the Year.
Under the scheme, the council can provide employers with up to £8000 towards the costs of an apprentice.
Gerry Doyle, 52, manager of the garage, said: "We can't get assistance for him because he was schooled in Bearsden.
"We have him four days a week and we've spent five weeks with him but we are going to have to put him out.
"The potential in the boy is immense.
"It's a G61 postcode, so it's still technically a Glasgow postcode.
"I can't get any help from East Dunbartonshire Council either.
"There are no other grants available. It is hard for us to take on apprentices. We are taking kids off the dole queue but getting no support."
The business was recently named Best Garage in a national awards scheme.
A spokesman for Glasgow City Council said: "We have supported this business in the past in the employment of apprentices.
"However, in this case, we are unable to do so as the young person does not live in Glasgow and did not attend school in the city.
"Since August 2009, we have placed almost 3000 young people in apprenticeships and jobs through the £25million Glasgow Guarantee, which comprises the Commonwealth Apprenticeship Initiative."