Behind the scenes rumblings in the Tasmanian Government have exploded into the open after backbencher Brenton Best called for Premier Lara Giddings to be replaced.

Mr Best told The Advocate newspaper: "I just can't see a way forward with the current leader."

The Labor backbencher has been openly critical of his party's power sharing deal with the Greens and has repeatedly attacked Greens Leader and Cabinet Minister Nick McKim.

Mr Best is touting the ambitious Economic Development Minister David O'Byrne as a good replacement.

Ms Giddings recently stated she would consider continuing with power sharing, if necessary, after the election in March next year.

It was the last straw for Mr Best, who is a member for the north-west seat of Braddon, which has the lowest support for the Greens in the state.

The MP reiterated to the ABC that it was time for her to go.

"This arrangement's not working. It's upsetting the average person on the street ... the truth is I think it's time to move on and I don't think we should do this again - it's been a failed experiment," he said.

"I think what we need is a different kind of leadership - one that's is more consultative, one that is not so dictatorial, one that listens to the community."

Giddings accuses Best of aiding Hodgman

In a statement, Ms Giddings said Mr Best had not raised his concerns with her.

"I find it odd that he instead chooses to air this issue through the media," she said.

"Clearly Brenton has to decide whether he wants to be part of Labor team united behind these objectives or whether he wants to throw rocks from the sidelines, effectively campaigning on Will Hodgman's behalf."

Mr Best says he has spoken to the Premier about his concerns, both in person and by letter, but not recently.

"For her to say that I've never raised these things with her, that's just simply not true and I totally reject those comments," Mr Best said.

Premier Lara Giddings says Mr Best had not raised his concerns with her. ( ABC News )

"I've had discussions with the Premier about this over the last three years and I've told her where I think things weren't right," he added.

"I've told her that she lacks my confidence on occasions on certain issues, I've told her that I didn't like the way she treated the public servants ... I told her that.

"I didn't agree with the cuts in elective surgery ... and basically she didn't want to hear it. So where do you go?

"I haven't really talked to her for over 12 months."

Mr Best says unlike previous Labor leaders, Ms Giddings does not listen to other people's views and claims she has a dictatorial style.

"It's serious. I've thought about it for weeks now," he said.

"I was disappointed when it was announced that we were all in lockstep behind the Greens if there was the chance of minority government in March next year and I don't support that.

"I think if my colleagues were able to reflect on it and they were given the choice in March next year they wouldn't be supporting an arrangement with the Greens again - it doesn't work.

"I disagree with her style of leadership - I've told her that.

"She should take it very seriously because it's not just me; it's the membership of the Labor Party ... people of the trade union movement, the community at large have had a gutful of this Government," Mr Best added.

Suggested replacement backs Giddings

Mr Best is touting the ambitious Economic Development Minister David O'Byrne as a good replacement.

"He's a person that doesn't compromise on traditional Labor values and he supports industry - Tasmanian industry - and I know he's not someone who would want to compromise himself by doing some sort of power deal with the Greens," he said.

However, Mr O'Byrne responded on social media, saying: "This kind of talk does not help Labor".

He says he backs Ms Giddings as leader.

Greens Cabinet Minister Cassy O'Connor says she is not surprised by Mr Best's comments, but they are disloyal.

"Ultimately the leadership of the Labor Party is for the Labor Party, but it is a bit rich coming from one of the biggest underperformers in Parliament calling for his leader to go," Ms O'Connor said.