A cordon has been put in place at Alexandra Park, in the Dennistoun area of the city, and the entrance at Provan Road has been sealed off by police as a precaution while they investigate the package.
The nature of the suspect item has not been disclosed.
A Police Scotland spokeswoman told the BBC:
"At about 8.10am, police received a report of a suspicious item within Alexandra Park.
"As a precautionary measure, a cordon has been placed around an area of the park."
She added: "The EOD (Explosive Ordnance Disposal) are currently at the scene to examine the item."