With Malcolm Turnbull currently governing in a minority, and a nail-biting byelection approaching in the Sydney seat of Bennelong, speculation has mounted over how the Prime Minister could shore up his numbers in Parliament.

One option would be to offer the speakership to Ms McGowan - just as former prime minister Julia Gillard installed LNP turncoat Peter Slipper as Speaker late in 2011 to prop up her flailing minority government.

Mr Turnbull and Ms McGowan enjoy a warm professional relationship and speak weekly. "We're very professional and we work well together," Ms McGowan said.

The independent Indi MP was elected in 2013 after narrowly defeating the controversial Liberal incumbent Sophie Mirabella.

Ms McGowan said she had "thought about" the prospect of becoming Speaker, fuelling speculation Mr Turnbull had made the offer. A spokesman for the Prime Minister said his conversations with parliamentary colleagues were always private.

"The answer is no," Ms McGowan said. However, she would make an exception on national security grounds, she said, "if the PM asked me for the sake of the nation".

"My community really like having an independent who speaks up for them," Ms McGowan said. "If you're a Speaker, you can't speak up for your community."

During the last term of Parliament, Ms McGowan sided with the government for 28 divisions, and the opposition 32 divisions. She voted against both sides nine times. She sided with the government to support 442 of the 475 bills passed by the House of Representatives.

The Speaker of the House is traditionally drawn from the governing party and does not vote unless to break a tie. Normally they do not attend party room meetings and do not partake in the day-to-day matters of politics.

"It would be a huge cost to my community to not do that anymore," Ms McGowan said.

The Turnbull government currently has 73 out of 147 votes on the floor of the House, with Tony Smith in the Speaker's chair, and Barnaby Joyce and John Alexander thrown out over dual citizenship. Mr Joyce, having easily won Saturday's byelection in New England, will soon return. Mr Alexander is expected to win in Bennelong on December 16, but the race will be much closer.

If Labor's Kristina Keneally were to snatch Bennelong, the government would be permanently reduced to 74 votes out of 149 on the floor. Ms McGowan and fellow crossbencher Rebekha Sharkie have said they will guarantee confidence and supply to the Turnbull government even if it enters minority.

The government's difficulties were illustrated on Monday afternoon when it embarrassingly lost a vote on the floor of the House. A Greens motion calling on the government to take up New Zealand's offer to resettle refugees from Manus Island passed with Labor and crossbench backing after Trade Minister Steve Ciobo and Liberal backbencher Warren Entsch failed to attend the vote.

A loophole allows the vote to be repeated on the grounds that the missing MPs were absent by "misadventure" rather than by design. The result was then overturned.