It is understood the family of 19-year-old Duncan Sim, who was last seen in the area of St Andrews Links, has been informed of the discovery at West Sands.
Duncan Sim and (right) an image from CCTV on the evening he disappeared.
The remains, found on Sunday, have not been identified and police said inquiries were at an early stage.
A Police Scotland spokesperson said: “At 6.25pm on Sunday June 3 officers from Fife attended West Sands, St Andrews, after the discovery of what is believed to be human remains were found within the water.
“Inquiries remain ongoing at this time.”
Duncan, who is from Duns in the Borders and is a keen sportsman, was last seen just after 11pm on Wednesday March 14 after leaving Madras Rugby Club.
The alarm was raised after the chemistry undergraduate failed to arrive back at his accommodation at Agnes Blackadder Hall.
Police said he ran off in the direction of Eden Clubhouse on St Andrews Links, where he was spotted on CCTV.
