A large group of the Rome club's fans were pictured walking up Buchanan Street, with many seen raising their right hand while chanting fascist songs.
The footage was posted on social media at around 5pm BST, ahead of the game at Parkhead which kicked off at 8pm.
It was reported on Wednesday that specialist anti-mafia police had been flown to Scotland in order to monitor the Lazio 'ultras', who have a reputation for fascist gestures and racist chanting.
Around 1,500 supporters are believed to have travelled from Italy for the game.
Watch: Video of the incident in Glasgow city centre.
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