The 33-year-old batsman, who underwent surgery on a troublesome hamstring in December, made 51 on his return for side Western Suburbs against Gordon.
Reports in the Sydney Morning Herald said Clarke had clashed with his country's selectors over the deadline they had given him to prove his fitness for the World Cup, which Australia are co-hosting with New Zealand from Feb. 14.
Even if he did return to health, the newspaper reported that his team mates had turned their back on the captain in favour of stand-in Steve Smith but Clarke said there were no problems.
"I'm not going to get into it. It seems like some people in particular are going to write what they're going to write," Clarke told reporters.
"I'm really happy and comfortable with my relationship with Cricket Australia firstly, certainly with my team mates so whatever.
"It's water off a duck's back for me. I've copped it my whole career so it's another day, another newspaper sold. I don't really care. My job is to get fit and healthy and I can't wait to get back on the park and play for Australia again."
Clarke has been given until Australia's second World Cup match against Bangladesh on Feb. 21 to prove he is fit to play a part in the tournament.
The combative captain is optimistic that he will be back at the helm for his country soon.
"I'm certainly ahead of where the surgeon and the Australian medical staff thought I'd be at the six-and-a-half week stage," Clarke said.
"The fact I'm back on the field playing is a really positive sign. I think the experts are saying I'm a good week-and-a-half ahead of schedule but it's one day at a time for me.
"My goal is to get fit as soon as I can. Then there is a timeframe set by Australia and the selectors that I certainly understand and respect."
(Reporting by Sam Holden in London, editing by Ed Osmond)
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