Officers received two separate reports of a male in his late teens approaching and inappropriately touching two females at Seaton Park near to the Hillhead Halls of Residence during September and October.
In addition another report has since been received about a similar incident on Wednesday November 2, 2016.
All occurred on or near steps next to the site between 4.30pm and 5.30pm, and officers believe the incidents are linked.
The man in question is described as white, between the ages of 17 and 20, around 5ft7-9 in height with short light brown or blonde hair. In each case he is described as wearing dark sportswear including a hooded top and jogging bottoms, and following the most recent incident he is believed to have a local accent.
Detective Constable Kirsty Munro said: “This is the third similar incident reported to Police in recent weeks and I would like to reassure the community that officers are taking these reports very seriously. Although none of the females involved have been hurt or injured in any way, they have been left feeling understandably concerned and uncomfortable.
“Uniformed officers will once again be giving particular attention to the area and I would urge people using the park to be on their guard. These type of incidents are extremely rare in the area - and the city generally - however by no means should that make anyone complacent.
“Anyone who recognises the description of the male provided and can assist with the investigation should contact Police on 101 with information, or the charity Crimestoppers on 0800 555111 if you would prefer to remain anonymous.”