The 31-year-olds were walking in Pitt Street near Bath Street at around 3am when a group of men attacked them.
The emergency services attended and the pair were taken to Glasgow Royal Infirmary for treatment to stab wounds.
Medical staff have said they are both in a stable condition.
Detective Constable Andrew Barbour said today: “Officers are continuing inquiries to establish more details on this incident and to trace the males responsible, this includes studying CCTV footage from the local area.
“At this time I would ask anyone who was in the area of Pitt Street around the time of the incident, who either witnessed this attack take place, or who has any information on the men responsible to come forward to police.”
A stretch of Pitt Street between Bath Street and Sauchiehall Street was closed to traffic on Monday morning, but and has since reopened.
Anyone with information on the attack is asked to call police on 101 or Crimestoppers, where information can be given anonymously, on 0800 555 111.