Daniel Nolan was fishing in freezing conditions
Pauline and Greg Nolan appealed to the public to try to find their 14-year-old son Daniel who went missing in Hampshire on New Year's Day.
He was last seen walking towards a pontoon on the River Hamble, at about 2330 GMT.
On Wednesday, rescuers scaled down their search of the area, which had involved a coastguard helicopter and a Royal Navy diving team.
However, in a statement released through Hampshire Police on Thursday, Mrs Nolan said: "We know that the police and coastguard have searched everywhere they can, and accept that he may have fallen in the water.
"But there is still a chance of Daniel being in the area.
"He may have become disorientated or been unable to get home and gone for shelter."
Daniel had been fishing with friends in freezing conditions but left to go to a shop.
When he saw his friends again, they told him they were going home because it was so cold.
Daniel told them he would catch up and set off towards the icy pontoon to pick up his fishing tackle.
He has not been seen since and police fear he may have fallen in the water and drowned.
Police were called at 0400 GMT on 2 January, when Daniel did not return to his semi-detached home in Hamble Lane, Hamble.
Daniel's gloves and fishing tackle were later found on the pontoon at Hamble Marina.
However, despite a massive land, air and sea search over the last 36 hours, Daniel has not been found.
On Thursday, officers were continuing to scour the area where he disappeared.