Cooper signed a new three-year deal with Queensland in June but has reportedly decided to walk away from the Wallabies and Reds after he was offered an incentive-based top-up deal by the Australian Rugby Union.
The 24-year-old, who was fined 60,000 Australian dollars by the ARU after labelling the Wallabies a "toxic environment" on Twitter last month, is believed to be considering a stint in boxing.
"I've got nothing. I haven't spoken to him, we haven't spoken to him as a union so I can't really tell you anything," McKenzie said of Cooper's future.
"I'm not going to speculate whether it's true or not. The information's out there, whether it's true or not I don't know.
"We'll just see what happens.
"I haven't heard from Quade so if I do that might give me some comfort but he knows I don't have any influence over the ARU [negotiations] so that's probably one of the reasons why he hasn't rung me about it.
"Queensland's done all it can do in terms of securing him for the long haul for Australian rugby, but it's out of our hands."
Cooper's AUD 400,000-per-season deal with the Reds will be deemed invalid unless the 2010 Australian Super Rugby player of the year can agree to terms with the ARU.
Negotiations broke down on Monday after the governing body withdrew their initial offer and replaced it with an incentive-based deal usually reserved for rookies.
"He's given us his word...and I spoke to him seven or eight days ago and as far as I was concerned I never felt that he was going to do anything other than play for the Reds, so that's how I'll approach it at the moment until somebody formally tells me otherwise," he said.
"We've made plans for next year around [Quade] and we're going to continue as if those plans are unchanged.
"If it changes that will be disappointing but at this point in time I've got nothing other than some stories that were put out last night and whether they're true or not we'll find out."
Reds and Wallabies scrum-half Will Genia added: "It would be a massive loss but at the end of the day I'm a close friend of his and I want him to be happy.
"He has to be happy and he has to be somewhere he feels as though he's respected and treated fairly.
"That's not to say I don't think he's getting treated fairly, it's just the way that he has to feel.
"I'd love for him to stay without a doubt. I love playing with him, there's no other [number 10] that I enjoy playing with and no other guy that I love having in my team more."
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