Arthur, who was sacked 16 days before the first Test at Trent Bridge, has claimed substantial damages, and leaked documents in Australia allegedly said he had described Clarke's former vice-captain Shane Watson as "a cancer" in the side.
"It's not distracting at all to me and the team," Clarke told a news conference on the eve of the second Test at Lord's which Australia must win to level the five-match series.
"I've spoken a lot in the past about my relationship with Shane and so has Shane, so I'm not going into that, and in this team right now it's about looking forward."
Clarke paid tribute to Arthur's successor Darren Lehmann who he said had been outstanding in galvanising a team who lost the first Test by only 14 runs after an awful start to their tour.
Before Arthur's dismissal, batsman David Warner was suspended for punching England batsman Joe Root in a Birmingham bar during the Champions Trophy.
Australia finished bottom of their group in that tournament.
"I think we showed all of the media and the public over the past five days playing at Nottingham and we'd like to continue showing that in the second Test at Lord's," Clarke said.
"Our focus is that we are as well prepared as we can be in regards to training today, and get out and enjoy this second Test match."
England captain Alastair Cook, whose side have won the last two Ashes series, said the Arthur controversy was irrelevant.
"You all saw what a tough Test match it was in Trent Bridge and what a close test match it was," he said.
"For us what goes on off the field is irrelevant, it's not for us to comment on.
"We have to concentrate entirely on ourselves."
Neither captain would disclose their final eleven for the Test.
England fast bowler Steven Finn was expensive in the Nottingham Test and he has Tim Bresnan and Graham Onions challenging for his place.
In Finn's favour is his fine Test record at the headquarters of his county side, Middlesex.
"You are looking at the best balanced attack for the conditions available," Cook said.
"With a hard, bouncy wicket you want a lot more pace.
"On a different wicket you want control and sometimes control can build pressure to take wickets.
"It's always interesting to find the right balance."
Clarke said he had not yet had an opportunity to examine the pitch, which showed a few traces of green when the covers were taken off on Wednesday afternoon.
But it will bake in the hot, sunny conditions forecast for the next five days.
"At this stage I haven't got an eleven from the selectors," he said.
"I think they want to look at conditions today and see what the pitch is like and then pick the team later on this evening.
So I'm not really sure what they are thinking."
Clarke said Australia were very proud of their record at the headquarters of world cricket, where they lost only one Test in the 20th century, and their spirited performance in Nottingham.
"It should inspire us to go one better," he said.
"Because we got so close it's given us that bit of inspiration."