Three fire crews spent almost three hours tackling a blaze from 0637 BST on Sunday at the stadium.
Council officers have now assessed the site on Ystrad Road in Fforestfach.
Greyhound racing ceased at the track late last year and the land has been earmarked as an employment site.
Mid and West Wales Fire and Rescue Service said no injuries were reported. The cause of the fire is still under investigation.
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