Unions say Glasgow Life staff - who also look after the city's museums - are treated as a "second-class workforce".
Unison, Unite and the GMB unions are balloting for a one-day strike in a bid to secure additional payments.
Glasgow Life is an arm's-length organisation with 2800 staff overseeing the council's publicly-owned leisure centres, museums and libraries.
The Evening Times understands 800 staff will be asked to give the go ahead for a walk out.
Brian Smith, Unison City of Glasgow branch secretary, said: "Glasgow Life is treating its staff as a second-class workforce and it's no wonder these workers feel undervalued.
"They are just as important to the delivery of the Games as other council workers and should be afforded the same deal.
"Those in charge of the Games should treat all workers with respect and recognise the crucial role they will play over the next couple of months."
The unions claim Glasgow Life has offered no "enhancements" for working overtime and also changed shift patterns without agreement.
Mr Smith added: "I can't believe they think they're going to get away with this. There's a growing anger among staff."
A spokesman for Glasgow Life said staff have been offered overtime payments and an extra day off.
He said: "We are deeply disappointed that there has been a call for strike action and would urge those who have a vote, to vote against industrial action."
The ballot opens today and will run until July 11.
SUBWAY WORKERS GET GAMES PAY DEAL - PAGE 12