A lifeboat was called to the scene at 07:20 GMT where a 20ft (6m) cabin cruiser, named Phoenix Hardy, was found between the pier and Porth Eirias.
The crew searched the waters in Conwy county for casualties but none were found.
North Wales Police said it was made aware of the vessel at around 06:00 GMT and is appealing for information.
Det Sgt Mark Bamber said: "We believe that the boat came into the area yesterday and entered the water in Conwy."
The RNLI said its search of the waters was "inconclusive".
HM Coastguard said it was "reasonably" confident that four men who were aboard the boat got off safely.
A spokesman added: "We continue to work with the police until we are satisfied that is the case."