Robert Edward Hind, 46, was reported missing from Dewsbury on Wednesday evening.
Today (Monday) detectives recovered remains in the area of the River Colne next to Colne Vale Road in Milnsbridge, Huddersfield.
An underwater search team, dog teams and specialised search officers are currently investigating the scene.
Supt Scott Wood said: “The remains recovered from the river and its banks will now be forensically examined and enquiries are currently ongoing to identify them.
“An address in Manchester Road in Huddersfield is also being searched as part of our investigations.
“Neighbourhood Policing Teams are conducting high visibility patrols in each of these areas responding to any concerns locally.”
Police had initially issued an appeal for information on Mr Hind’s whereabouts on Friday.
A 46-year-old man from Milnsbridge was arrested on suspicion of his murder yesterday (Sunday) and is still in custody.
Earlier today officers released CCTV images showing the last confirmed sighting of Mr Hind.
Supt Wood said: “It is imperative that we quickly ascertain the movements of Robert Edward Hind from Wednesday December 11.”
The CCTV images show Mr Hind with another man at Huddersfield bus station on Wednesday on at 9.20am.
Supt Wood said: “The man seen with Hind at Huddersfield bus station is described as white, around 5ft 5in tall wearing black trainers, jeans, a black jacket with a white hooded jumper underneath and was carrying a blue rucksack. He was also wearing a cream coloured beanie style hat.
“Hind himself was wearing black running shoes with white soles, dark coloured trousers, a khaki green coloured jacket and a dark beanie style hat. I would ask that anyone who recalls seeing the pair together at this time, or has seen either man since, to get in touch immediately.
“I believe the focus of this enquiry remains local and we need the public’s help to develop a full picture and bring about a swift conclusion to this matter.
“If you have any information as to Hind’s current location, however significant you believe it to be, please get in touch as a matter of urgency.”
Phone West Yorkshire Police on 101 or alternatively contact Crimestoppers anonymously on 0800 555 111.