It is understood detectives are following a positive line of enquiry in relation to the incident in Waterloo Lane on Saturday night.
The street was cordoned off with police tape and an officer standing guard yesterday afternoon.
Last night, police would not confirm the time of the attack or whether the victim was male or female.
The serious sexual assault is believed to have taken place in the early evening.
A spokesman said: "Police are currently investigating reports of a serious sexual assault in Waterloo Lane, Glasgow, on Saturday, March 28."