Institute Tasmanian director Leanne Minshull said Mr Gutwein had shown "good" leadership throughout the COVID-19 pandemic and could continue that strong approach by leading a national discussion.

And Independent Murchison MLC Ruth Forrest, who was a member of a taxation review team formed in 2010 but abandoned a year later, agreed the time was right for reform.

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Ms Minshull said Mr Gutwein should take Tasmanian taxation reform to National Cabinet.

"Mr Gutwein has the chance to continue his good leadership coming out of the pandemic crisis," she said.

"He could take it to National Cabinet and look for a national response.

"Mr Gutwein could argue for payroll tax harmonisation across the country rather than having the lowest bidder winning.

"We don't know what deals are done by other states on payroll to get companies to invest."

Ms Minshull said it was imperative that taxation inequality was discussed as part of the economic recovery from COVID-19.

"Like other states, Tasmania is limited in the types of taxes it can levy to raise revenue to pay for the services its citizens rely on," she said.

The current economic downturn means that now more than ever, that narrow base of taxes are as efficient and as fair and equitable as possible."

She believes the commonwealth would be keen to listen to Tasmania's arguments.

"I'm sure they would help through any transition phase and why wouldn't you ask them?" Ms Minshull said.

Ms Forrest, who has not yet read economist Saul Eslake's report he prepared for the Australia Institute, said his reforms were what she had called for for some time.

"We need to look at taxation reform in a non-partisan way," Ms Forrest said.

"Tax reform is never a popular conversation but now is the time as we struggle to recover from the pandemic and find the most fair, efficient and equitable system for our state.

"We can't do it without the commonwealth and there are always winners and losers and we would need help to transition to any changes."