MELBOURNE (Reuters) - Indonesian President Joko Widodo said there will be "no compromise" to his country's sovereignty in the contested South China Sea, ahead of a visit to staunch U.S. ally Australia.

The comments come after Australia's foreign minister, Julie Bishop, on Tuesday said the two countries were considering joint naval patrols in the contested waters.

China claims almost the entire South China Sea, through which about $5 trillion worth of trade passes each year. Brunei, Malaysia, the Philippines, Taiwan, Vietnam and Indonesia also claim part of the sea.

"In regards to Indonesia's sovereignty, I don't compromise. I don't compromise," Widodo told the Australian Broadcasting Corporation on Saturday.

Indonesian warplanes staged a large-scale exercise last month in the waters around the Natuna Islands archipelago, following a spate of face-offs between the country's navy and Chinese fishing boats in the gas-rich southern end of the South China Sea.

China, while not disputing Indonesia's claims to the Natuna Islands, has raised Indonesian anger by saying the two countries had "overlapping claims" to waters close to them, an area Indonesia calls the Natuna Sea.

Australia has previously drawn criticism from China for running surveillance flights over disputed islands in the South China Sea and supporting U.S. freedom of navigation exercises there.

Widodo will hold meetings with Prime Minister Malcolm Turnbull on Sunday amidst warming ties and a renewed push for a bilateral trade agreement between the two neighbors, expected to finalised next year.

The relationship between Indonesia and Australia reached historic lows under former Prime Minister Tony Abbott, who Turnbull ousted in a party room coup in September last year.

(Editing by Leslie Adler)