The incident is alleged to have taken place as the Besiktas squad travelled to Rhodes, Greece, for a mini-tournament earlier this year.
Reports, which originate from German newspaper Bild, claim that several members of the Besiktas youth squad have been suspended on the back of the alleged incident.
The ages of the players in question have not been revealed, although reports suggest that the players involved were all born in 2003.
Members of the squad are reported to have hired prostitutes during their time in Rhodes, with their female companions staying the night.
However, it is claimed that they were only caught out by Besiktas' coaches when they invited the women down to breakfast the following morning.
Bild claim that some parents of other players not involved in the scandal were also staying in the hotel and witnessed the females being brought down for breakfast.
One parent reportedly said: "We were all really shocked. That doesn't fit with the image of football. This is nothing about discipline."
It is claimed that all of the players involved in the alleged incident have been suspended by Besiktas.
Local rivals Fenerbahce are now reportedly considering helping the players restart their careers by offering them places in their youth team.
It is unclear how many young players were involved in the alleged incident.