It follows a series of indecent assaults in the past two weeks.
On each occasion women have been followed by the man while walking into the common close of blocks of flats before being indecently assaulted.
The first incident happened on January 24 at about 4.20pm when a 23- year-old woman walked into a close of flats in Great Western Road.
She was followed from behind by a man who attacked her and then ran off.
In a second incident, on January 31 at about 6.25pm, a 19-year-old woman was walking into a close of flats in Arlington Street when she was followed by a man who indecently assaulted her.
And in a third attack on Sunday at about 5pm, a 20-year-old woman was sexually attacked in a close in Kersland Street.
Police have confirmed they believe the incidents are all linked to the same man and extensive enquiries are under way to track him down.
Chief Inspector Alan Gibson of the West End Police Office said: "These incidents were frightening for the women concerned.
"We are continuing enquiries in the local area including viewing all available CCTV in an effort to identify the man responsible, and we have been deploying extra officers to provide public reassurance."
The suspect is described as white, aged 20-30, 6ft to 6ft 2in, and slim with black hair.
On each occasion he has been wearing a black top, possibly a hooded top and black or dark trousers.
He is also described as wearing a black beanie hat in two of the occasions and a black skip cap in one of them.
Chief Inspector Gibson added: "I appeal to anyone who may have witnessed a man fitting the description, acting suspiciously around the areas and times of the incidents, to get in touch. It is imperative we trace this man."
Anyone with information is asked to contact police on 0141 535 3350 or Crimestoppers on 0800 555 111.