Fowler, 34, signed a two-year contract with the new A-League franchise in February although he has yet to make his debut or even taken part in a full training session due to a string of groin and hip injuries.
But despite his lack of match practice after his three-month contract with Blackburn expired in December, Fowler has been linked with a move to Prenton Park where former Celtic and Jamaica manager Barnes is now at the helm after taking over from Ronnie Moore last month.
Jason McAteer, a former Liverpool team-mate of Barnes and Fowler, is also employed as Barnes' assistant at Tranmere, who just missed out on the League One play-offs last season on the final day.
The report suggested Fowler's family has also failed to settle in Australia and that, coupled with his succession injuries, would force his return to England.
But the former England and Manchester City striker insists he is staying put ahead of North Queensland's season opener against Sydney FC on August 8, although it remains to be seen whether Fowler will feature at Dairy Farmers Stadium due to his latest injury setback.
"I don't know where it's come from," said Fowler. "It looks like somebody's put two and two together and come up with six.
"I've got a two-year contract with North Queensland Fury FC and I'm a man of my word - I'll play it out.
"I wouldn't want anyone to do that sort of thing to me and I certainly wouldn't do it anyone.
"There's nothing to this - my family has just arrived and they wouldn't have travelled all this way if I had any intention to leave."
Fury coach Ian Ferguson has also spoken to Fowler, who scored 183 goals in 369 appearances for Liverpool, at length about the report.
"Robbie's happy here and he want to play football for the Fury," Ferguson said.
"There's no doubt he's the sort of player other clubs would be interested in, but John Barnes would have had to come through the Fury if he was interested in Robbie and that hasn't happened.
"Robbie is under contract to us for two years and it would be a breach of FIFA regulations for another club approached him.
"There's no one quoted in the story and it just isn't right.
"When you've got a world class player in your team there's always going to be speculation about him going to other clubs."