Former assistant treasurer Arthur Sinodinos says the GST base should be broadened.
Treasurer Joe Hockey has asked his department to cost a move to exempt feminine hygiene products from the GST, which he will take to a meeting with his state counterparts in July.
Mr Hockey is also under pressure to change the way the GST is distributed to the states.
Senator Sinodinos as chief of staff to former prime minister John Howard was involved in the design of the GST.
The Liberal senator said there were debates at the time about what was and was not health-related, which led to some examples of "rough justice" in the tax system.
However, he said making small changes to the GST would not be useful.
"The challenge for us today is not to be reducing the GST base. It's about how we can expand the base and use that to potentially help fund other tax reform," Senator Sinodinos told Sky News on Wednesday.
"I think the base should be broadened."
Labor says that if the government wants to exempt feminine hygiene products it should also extend the GST to digital downloads to ensure the revenue base is not undermined.
Treasurer Joe Hockey said there were many different views on the tax system which had to deal with all the needs of a 21st century economy.
He said he had asked Treasury to cost the removal of the GST from tampons and sanitary products and then seek the view of the states, which must unanimously agree to any changes.
"If their view... is unanimous that they want to remove the GST from sanitary products, then we are happy to take that through the parliament," he told ABC radio.
Mr Hockey said arguments on removal of the GST from other items should be considered in the government's tax review.
"If the argument about sanitary products turns into a debate about what should be in the GST or outside the GST, that's not about addressing an anomaly. That is about a much broader issue which is much better suited to the taxation paper," he said.
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