The state struck a deal with the Wagner Corporation to build the 1000-bed camp near Toowoomba in 2021.
Premier Annastacia Palaszczuk has for months refused to reveal the cost, saying it was "commercial-in-confidence".
While the state government on Wednesday announced it had spent $48.8 million on building Wellcamp, the full cost remains unclear with Treasurer Cameron Dick saying the lease is confidential.
He says the arrangement is no different to the former Liberal National Party government's confidential lease of the state government's office headquarters.
"That's a lease deal that they entered into that is commercial-in-confidence, so it's no different to that," Mr Dick told reporters on Thursday.
The Liberal National Party have written to state Auditor-General Brendan Worrall asking him to probe the Wellcamp project.
LNP finance spokesman Jarrod Bleijie said taxpayers deserve to know how much was spent and if the procurement process delivered the best value for money.
He's also asked Mr Worrall to probe whether keeping the lease cost secret was in line with government disclosure policy.
"It should never, ever have been commercial-in-confidence," Mr Bleijie said.
"There was no tender, there was no competition, it was direct funding."
"And Treasurer Dick and Premier Palaszczuk seem to think that this money doesn't have to be accounted for, doesn't have to be explained.
"Well here's the message to them: it's not their money, it's Queensland taxpayers money."
The government revealed the building cost of Wellcamp after Ms Palaszczuk said she would if the Commonwealth did so for another quarantine facility at Pinkenba.
The 800-bed facility near Brisbane Airport is being built jointly by the state and federal governments.
The Commonwealth revealed its $350-$400 million price tag on Wednesday, prompting the state to unveil the build cost of Wellcamp.
Mr Bleijie said the state treasurer needed to reveal the full cost, including the lease.
"I'd say this to Treasurer Dick: the federal government have shown you theirs, now you should show them yours," he said.
Earlier on Thursday, Health Minister Yvette D'Ath said with the upcoming federal election, Pinkenba was unlikely to open before April, if at all.
"We've waited for two years for them to get off their backsides and help us with hotel quarantine and manage isolation, and they've done nothing," she told reporters.
Ms D'Ath said the Wellcamp tender process was run by the Department of State Development, Infrastructure, Local Government and Planning.
She said journalists should refer to Deputy Premier Steven Miles, and refused to say whether Queensland Health was involved.
The minister insisted the government complied with "a whole range of procurement processes" and warned journalists about making "accusations".
"Certainly put those questions and get that information before we go down that rabbit hole," Ms D'Ath said.
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