A lifeboat attended the scene at 7.20 am and the crew searched the water for casualties after the vessel was seen between the pier and Porth Erias, but did not find any.
HM Coastguard said it was “reasonably” confident that four men who were aboard the boat got off safely.
Detective Sergeant Mark Bamber, from North Wales Police, said: “We believe that the boat came into the area yesterday and entered the water in Conwy. The boat is called Phoenix Hardy.
“We are appealing for the owners or the people who have any knowledge of the boat to contact North Wales Police on 101 quoting reference number A039123.”
North Wales Live reports that the boat has now been cordoned off on Colwyn Bay beach.
In a statement on social media, RNLI Llandudno said: “The cruiser was close to shore and found to be abandoned, at the request of HM Coastguard Holyhead the inshore lifeboat [ILB] proceeded to conduct a search in the bay to ascertain whether unknown casualties may have entered the water.
“After an inconclusive search the crew returned to shore to report to the waiting coastguard and North Wales Police.
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