"Winning back the Ashes is at the forefront of everybody's mind. I'd be lying if I didn't say that we were trying to build a really competitive team to go back and win them in 2013," the Australian coach said.
"Judging by reports that I've read they have started to take a little bit of notice," he added.
Australia has had a stunning revival after their 1-3 Ashes defeat last year and Arthur was confident his team won't be any pushover when they tour England in 18 months time.
Australia drew in South Africa last November and have already reclaimed the Border-Gavaskar trophy even before next week's fourth Test in Adelaide and Arthur said World No. 1 England is firmly on their radar.
"It is the ultimate goal," he said.
"Every series for us has been along the way though. We've prioritised series. This for us, this Indian series, was a World championship cricket series for us.
"The South African series here early next summer is going to be a huge series and we need to be able to win those series against those types of opponents, opponents ranked higher than us in the world, in order to go back into England and challenge," he added.
Australia will play England in 10 back-to-back Tests across two continents from mid-2013 to January 2014 and Arthur feels there is still a lot to be done.
"We haven't got anywhere near the heights that we want to. We've got to stay humble, we've got to stay working extra hard. There's a lot of areas we need to keep working on and get better at because ultimately we want to get back to No. 1 in the world," he said.
"We can't get ahead of ourselves. In the greater scheme of things we've won the series but we haven't won the war. I want to keep raising the bar."