Tasmanian business have urged Ms Hickey to remain in the Liberal Party saying they are "horrified" at the prospect of a minority government if she becomes an independent.

Ms Hickey took a swipe at Mr Hodgman's leadership saying the government was "directionless, lacked a strategy and is not addressing serious problems such as health and housing".

Mr Hodgman was unperturbed and said he had the "support and confidence" of his colleagues.

"I'm not concerned about personality politics," he said.

"I'm concerned about delivering for our state. My focus is on ensuring we as a government remain focussed on the people who elected us and not other politicians.

"The important thing to note is that Sue Hickey herself has said that she will continue to support the government, that she'll continue to support supply and she has expressed confidence in the government."

"So we continue to govern in majority and we are determined to do what we were elected to do."

Mr Hodgman hoped Ms Hickey would remain in the Liberal Party but did not elaborate on whether he would try to talk her out of leaving.

"Of course I will always talk constructively and positively with my colleagues about how we can best do that which we were elected to do, to spend more time talking about the people who elected us and less time talking about ourselves," he said.

Tasmanian Chamber of Commerce and Industry chief executive Michael Bailey said business wanted "stable, majority government" and Ms Hickey becoming an independent would not be good for Tasmania.

"We understand Ms Hickey's disappointment at being overlooked as a Cabinet Minister," Mr Bailey said.

"However, we also see that she is extremely important and effective as the Speaker of the House of Assembly.

Launceston Chamber of Commerce executive officer Neil Grose said business "would be horrified at the prospect of the Tasmanian parliament once again being hamstrung by minority government."

"Sitting as an independent and putting the government into a minority situation will seriously impact on business confidence at a time when Tasmania is doing well, with the state on a strong and sustainable growth trajectory.

"Business relies upon the stability of parliament for the confidence to invest and grow the state's employment and prosperity.

"It was self-evident during the long years of minority government that business investment deserted Tasmania for better economic conditions elsewhere.

"Tasmanians voted for majority government and this state has come a long way over the past five years of stable majority government: there is too much at stake to jeopardise the state's future."

Ms Hickey will consider her future this week and remains disappointed she has again been overlooked for a cabinet spot.

"It has been a problem being part of the team since I was pre-selected," she said.

"I was promised a ministry and I stepped down from a successful business I had run for 26 years and being Lord Mayor, a job I loved."

She said she had no regrets about accepting the position of Speaker and believed she had been effective.