Contractors doing enabling works at the site of the new National Indoor Sports Arena and the Velodrome had to down tools over a week ago, according to the Daily Record.
It is thought that it will take another two weeks before the work can resume.
A Glasgow Council spokesman said: "During this preconstruction phase to prepare the land on the site of the National Indoor Sports Arena, minute traces of asbestos were found buried in the ground in two locations.
"Work on the site has stopped as a precautionary measure.
"An investigation is currently taking place to establish what further remediation work will be necessary to allow work to restart.ADVERTISEMENT
"It is hoped the preparatory work will begin again in around a fortnight, with some chance this could start before.
"The National Sports Arena and Velodrome is being delivered in two phases.
"The first is an enabling works contract to prepare the site in advance of the main works contract to ensure any contamination from past uses can be dealt with."
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