A plan by a Federal Government minister to poach cricket Test matches from Tasmania for his electorate on the northern coast of New South Wales is gathering momentum.

But Tasmania's Premier has warned him to back off.

Tasmania will host its first Test match in three years when Australia takes on the West Indies at Bellerive Oval next month.

It is the first Test since Sri Lanka visited in 2012.

But concerns have been raised about the prospect of Tasmania losing hosting rights for future Test matches due to poor attendance.

Federal Minister for Vocational Education and Skills Luke Hartsuyker said comments attributed to James Sutherland from Cricket Australia indicated attendances in Tasmania were not as strong as they could be.

"I would say to all Tasmanians if you want to keep your local Test turn up and watch and enjoy great quality cricket and if you're not going to do that, well we'll be happy to take the Test up in Coffs Harbour," he said.

He said he had written to Cricket Australia offering Coffs Harbour as a potential alternative venue to Bellerive Oval to host Test matches but was yet to receive a response.

But Premier Will Hodgman hit back.

"Coffs Harbour doesn't have a beautiful ground like Bellerive, it doesn't have the rich cricket tradition that has produced legends of the game like Ricky Ponting and David Boon," he said.

"Our state is part of the national cricket fabric and and they are well within their rights to go off and try and get a Test match of their own, they're not having ours."

Mr Hartsuyker has been in Hobart to meet state skills ministers and admitted his stance on commandeering a Test match from Tasmania was not a popular one.

"A robust exchange of views is probably a good way to put it, I must say that your local parliamentarians here are very protective of Tasmania and sticking up for the interest of Tasmania just as I am very keen to stick up for Coffs Harbour," he said.