Labor leader Gillard likely will push Indonesia to make stronger efforts to curb the activities of high-level criminals who organize unseaworthy ships full of would-be asylum seekers hoping to reach Australia.
But Susilo also will have demands, including for Australia to take more bona fide refugees, The Age reported.
The issue of people smuggling has been a highly visible issue for both countries for at least a decade. Thousands of people -- mostly from countries other than Indonesia -- pay smugglers large sums of money for passage on leaky vessels.
Many reach Australian waters and the lucky ones are rescued by the coast guard. The unlucky ones drown when their vessels sink in rough seas or break up on rocks.
People smuggling, overflowing refugee detention centers and illegal immigration are emotive issues in Australia and a minefield for its politicians in the run-up to September's federal election, expected Sept. 14.
Australia has thousands of asylum seekers in detention centers awaiting processing and they keep coming, despite people smuggling being illegal in Indonesia.
But this week The Age published a report that suggested some Indonesian police are working with the smugglers.
A hidden camera caught suspected people smuggler Freddy Ambon saying police near one of Jakarta's ports are "my men," The Age reported.
Johnny Hutauruk, head of the Indonesian government agency Human Trafficking, Refugees and Asylum Seekers, said Australian diplomats have asked him to beef up surveillance of suspected people smugglers and he has done that.
Hutauruk said Australia could ease the problem in Indonesia by taking 2,000 instead of 600 refugees a year through the United Nations High Commissioner for Refugees.
Australia's opposition coalition said if it were to win the next election, it would take less, not more, refugees under UNHCR plans, The Age reported.
Last week Gillard faced angry opposition members of Parliament during question time. They said she should apologize to Indonesia when she arrives there for making Australia a soft touch for asylum seekers and not sending them back.
This encourages more people to pay the notorious people smugglers for an often deadly passage in rough seas.
Tony Abbott, leader of the main opposition Liberal Party, said he stands firm on the opposition coalition's policy of returning boats to Indonesia rather than putting the passengers in detention centers.
"These are Indonesian boats and an Indonesian boat is entitled to return to the port from which it has come," Abbott said.
Australian Green Party leader Christine Milne said Gillard's trip to Indonesia is "a last-minute effort in the context of an election campaign."
Indonesia also faces criticism related to its detention centers, in particular how it treats children in them.
A report by Human Rights Watch said hundreds of children every year are kept in squalid conditions, denied lawyers and sometimes beaten or thrown out onto the streets with no place to go.
Indonesian presidential spokesman Teuku Faizasyah denied the allegations in an interview with Radio Australia this week.
"I've never heard of such accusations," he said. "Cases might happen, but that's not systematic. We didn't design our facility to deal with so many people."