Authorities and the family of a 64-year-old Mosman Park man who went missing while swimming at Cottesloe Beach on Monday feared he was attacked by a great white pointer based on the tear on his bathers found by police divers.

The wife of Bryn Martin identified the Speedo bathers as the type used by the accomplished swimmer and chief executive of James Point, a private port builder.

"Fisheries experts have viewed the bathers and were of the opinion the damage is consistent with that a white pointer shark could cause," said duty patrol commander Neil Blair, according to Perthnow.com.

Police divers suspended their search and recovery of Martin's body on Tuesday due to risks posed by the murky beach water. Cottesloe Beach was also temporarily closed until Wednesday.

Martin was swimming alone several hundred metres from the shore in front of the Indiana Tea Rooms at about 8 a.m. on Monday. A friend who joined him in the water called the police after Martin did not surface for about 10 minutes.

Martin compose the oldest swimming duo, who achieved the feat during their Rottnest Channel Swim performance in 2002.