The Sydney Morning Herald claimed they disagreed over a deadline for proving Clarke's fitness for the World Cup, which begins on 14 February.
Clarke, 33, made 51 playing grade cricket for Western Suburbs on Saturday on his return from hamstring surgery.
"I've copped it my whole career. It's another day, it's another newspaper sold. I don't really care," he said.
"Some people are going to write what they want."
Batsman Clarke has not played since having surgery on a hamstring injury sustained in the first Test against India in December.
In January, he was named in Australia's 15-man World Cup squad, on condition he proved his fitness in time for their second group game against Bangladesh in Brisbane on 21 February.
Clarke is reported to think their fourth match against Afghanistan in Perth on 4 March is more realistic.
However, he said: "I'm really happy and comfortable with my relationship with Cricket Australia, firstly, certainly with my team-mates, so it's water off a duck's back.
"My job is to get fit and healthy and I can't wait to get back on the park for Australia.
"I'm certainly ahead of where the surgeon and the Australian medical staff thought I would be at the six-and-a-half-week stage."
In Clarke's absence, Steve Smith has excelled as stand-in captain, winning the Allan Border Medal and claiming Test and one-day player of the year accolades at Australia's annual cricket awards.
Australia captain Michael Clarke has dismissed reports of a dispute with Cricket Australia.