Michael Palfrey, part of the Australian coaching team in Paris, told South Korean media he hoped Kim Woo-min won gold instead of Sam Short and Elijah Winnington in the men's 400m freestyle.
The trio -- all former world champions -- will face off on Saturday in the opening day of action at La Defense Arena.
"Very disappointed, extremely disappointed," Australian head coach Rohan Taylor said. "For a coach on our team to promote another athlete ahead of our athletes is not acceptable."
Palfrey works with Australian swimmers Zac Incerti, Abbey Connor and Alex Perkins, but also mentored Kim while he was training in Brisbane ahead of the Games.
According to The Sydney Morning Herald, Palfrey was wearing Australian team colours when he was interviewed by South Korean journalists and declared "Go Korea" while talking about his hopes for Kim.
Taylor said he needed to make a "pragmatic" decision "sooner rather than later" about whether Palfrey stays on the team, balancing the needs of his swimmers with discontent in the squad.
"Promoting an athlete who is not Australian is un-Australian to be honest," he said.
"The options are he either goes home or he stays, and what is the impact on the performance of the team.
"If he goes home we have to find other coaches to pick up the load and our coaches are really stretched.
"If he stays, it's about the team dynamic and whether the other coaches can support that and the athletes can go about their business and not be distracted."
Australian chef de mission Anna Meares called Palfrey's comments "a serious error of judgement".
"Like a lot of people, it was a surprise and a shock. My first thoughts went to the athletes and the welfare of the athletes," she said.
Zac Stubblety-Cook, who is preparing to defend his 200m breaststroke title, spoke to Winnington and Short on Thursday and said they "weren't super fazed to be honest".
"Yes, it is disappointing but it hasn't rocked the boat too much," he added.
