Dual world middleweight champion Daniel Geale's next major goal is to conquer boxing's biggest market in the United States.

To start that process, Geale plans to introduce himself to the American media by attending the September 15 WBC middleweight title bout between champion Julio Cesar Chavez Jr and Sergio Martinez, who is widely regarded as the best fighter in the division.

Back in Australia less than 48 hours after dethroning WBA Super champion Felix Sturm in Germany to add the WBA title to the IBF one he won in the same country, Geale was adamant he was still far from his peak and was bent on tackling even harder, bigger fights.

"I think if you go over and conquer the US as well that's the next target," Geale told reporters.

"With the help of my promoter Gary Shaw, we're going to get over there and shake those guys up too.

"It's been great to do it in Germany, but I think now we've got to do it in other countries as well.

"I'd love to be able to bring some huge name fighters out to Australia as well.

"I'd love to be able to put on a massive home town fight in Sydney, it would be unbelievable.

"We've got to keep taking the next step and that is obviously going to mean more money, but it definitely means harder and bigger fights."

Geale said the winner of the Chavez Jr-Martinez fight and his own mandatory title defences against fellow Australian Sam Soliman (IBF) and Kazakhstan's KO specialist Gennady Golovkin were all options for his next bout, which he hoped to have by December.

He said he would also love to have a rematch with compatriot Anthony Mundine, the only man to beat him in 29 professional contests.

"It's always been open on our side. We've always been happy to jump in there, but it seems to not happen," Geale said.

Geale produced the best performance of his career against Sturm and said he still had a lot of room for improvement.

"I've always wanted to get better, I think that's the reason why I keep improving and I still believe that I've still got so much more to go," Geale said.

"I don't think I've reached the pinnacle at this stage yet, I've got heaps of improvement in most areas.

"I believe I could still be faster. I believe I could still be stronger."

Geale said he was under no obligation to give Sturm the rematch he wanted and revealed his opponent's pre-fight arrogance had provided him with more motivation.