Paul Arber, 38, was last seen swimming in the river at 4am on Sunday by a pair of passersby, police revealed this afternoon.
Waikato Field Crime Manager Detective Inspector Karl Thornton said the pair convinced Mr Arber to get out of the water.
However, Mr Arber then changed his mind and went back into the river.
Mr Thornton said Mr Arber's behaviour was out of character.
He had been described as acting "distant and spiritual" in the hours before his disappearance.
Police were still looking to speak to a homeless man who Mr Arber gave money to and a couple walking their dog who spoke to him.
Mr Arber's parents had arrived from Australia and were "extremely concerned", Mr Thorton said.
Mr Arber is a director and partner in Trademark Tennis in Melbourne.
The company's website said he had worked with the Australian Institute of Sport and The National High Performance Academy, and coached elite juniors and professionals including Monica Seles and Caroline Wozniacki.
Fellow director Asar Nagar told the Herald Sun newspaper that he had taken a small group of teenage tennis players to Hamilton for a tournament. "We're just hoping for good news," he said.
Another coach and friend, Julian Arnold, said Mr Arber was among the top few hundred players in Australia, and ran tennis tours for young players to New Zealand the US. "He's a great guy, there's nothing bad to say about him," he told the Herald Sun.
"It's pretty devastating news."
Hamilton police yesterday had a caravan in Hamilton East with a mannequin wearing clothes similar to the tracksuit Mr Arber was wearing when last seen.
Mr Arber's wallet and keys were found on Cook St while his luggage and passport were left in his accommodation.
Detective Inspector Karl Thornton said yesterday that the coach had been seen to stop and pat the dog of a couple who were out walking their pet just before he disappeared.
He had also stopped to speak to a man described by witnesses to be a homeless person who police believed he gave some money to.
Police appealed for the couple and the man to come forward.
"We are becoming increasingly concerned that we have not heard from Mr Arber. He is not familiar with the area and does not know anyone in Hamilton," Mr Thornton said.
Mr Arber is described as a slightly built Caucasian, 179 centimetres tall (5 foot 9 inches) with short, dark hair.
He was wearing a grey tracksuit with a tennis logo on the left breast of the top and a Wilson tennis logo on the left shoulder of the top.
Any information which may help in locating him can be provided to Hamilton police station on 07 858 6200 or anonymously through Crimestoppers on 0800 555111.
- Heather McCracken of APNZ
