The alarm was raised at around 5pm this evening.
Officers rushed towards the scene at the area around Buchanan Street Subway station, which was busy with shoppers on the last Saturday of the year.
A thorough search for the man was conducted but no one was traced.
Buchanan Street Subway station was evacuated and closed off while police carried out a search.
The station has since reopened.
Police are continuing their search by reviewing CCTV footage from the area.
There no reports of any injuries to the public.