Dannii Minogue (right) has said she is "very optimistic"

A statement on Thursday said Kylie would have an operation "this week".

Dannii, also a pop singer, arrived from London on Friday and headed to the family's home, where her sister has been staying, according to local media.

Meanwhile, Madonna has added her support, saying: "Kylie's a fighter and I know this is a battle she will win."

Kylie is expected to have the surgery on Friday or Saturday. She is being treated by "one of Australia's leading surgeons", her statement said on Thursday.

Madonna famously wore a Kylie T-shirt at an awards show in 2000

"Thankfully tests so far have confirmed the earlier diagnosis that the cancer appears to be confined to the breast."

Madonna has added her voice to thousands of fans and stars including Sir Elton John, Delta Goodrem and Olivia Newton-John who have wished her well.

"I was saddened to learn about Kylie Minogue's breast cancer diagnosis," Madonna's statement said. "I'm so grateful that they found it early.

"Let's all pray for her speedy recovery and send all of our best wishes her way. With love and light to you Kylie."

Kylie's fellow Australian singers Goodrem and Newton-John have both fought battles against cancer.

Newton-John told the media, who have camped outside the family home and hospitals, to respect Kylie's privacy.

Kylie's fans and media have gathered outside her family home

She said: "This is not the time to be hanging at her house - you need to leave her alone."

She added: "It's a wake-up call for women that we need to self-examine on a regular basis and there is no age limit."

Kylie, 36, has thanked her fans for the outpouring of support.

"My heartfelt thanks to the incredible number of people who have sent messages of love and support over the last two days," she said on Thursday.

"I want to reassure you that I am being well taken care of."

Her boyfriend, French actor Olivier Martinez, was by her side and she said she had "a lot of family and friends around me".