Police have told relatives of the five rugby players swept out to sea in Port Elizabeth to accept that their relatives are dead, Beeld reported on Tuesday.
"You must accept that they are no longer alive and be prepared for what may happen," the paper quoted Captain Anton Groenewald, from the Swartkops police station, at a counselling session with local residents.
"It can be weeks before the bodies wash up, and it is possible that they may never emerge," he said.
Captain Andre Beetge said the session was intended to mentally prepare the families.
He said the police had not given up the search, and were putting more resources into finding the men.
These include two border patrol vehicles and a sonar device that was coming from Gauteng.
Counsellors and social workers were also being sent to help the relatives and the victims' fellow players.
According to Beeld, four of the five Motherwell Rugby Club members still missing had been named as Xolisa Nyembezi, 27, Arthur Peters, 30, Lundi Muleka, 29, and Avuyile Tshabalala, 18.
The fifth man could not yet be named as his family had not been informed.
The body of one of their teammates, Msixole Myosana, 29, was pulled from the water on Sunday.
Groenwald was further quoted as telling relatives: "I'm sorry to say this, but it is also possible that sharks and other sea creatures have mutilated the bodies, and you must be prepared for this."
The players apparently took to the water to cool down after rugby practice on Sunday, but were caught in a rip current.