A cordon is in place around the building, on George Square, after a report of the package at around 3.20pm today.
A Police Scotland spokesperson said: “Police received a report of a suspicious package at the City Chambers, George Square, Glasgow around 3.20pm on Monday, 21 February, 2022.
“Officers are in attendance alongside other emergency services and a cordon has been put in place.
“Part of the building has been evacuated as a precaution.
“Enquiries to establish the full circumstances are ongoing.”