Redford, in an interview Friday, said while Finance Minister Doug Horner has recently mused publicly about such alternative funding programs, Alberta's tight finances won't allow it.
She said Edmonton, like all communities, can fund the project using provincial infrastructure grant money through the multibillion-dollar Municipal Sustainability Initiative, known as MSI.
"Every community in this province can make the decision that it wants to in terms of their community priorities with MSI funding," said Redford.
"But in terms of other streams of funding it's not something that any community should be contemplating, particularly in these fiscal times."
On Thursday, Redford announced that falling prices for oilsands bitumen are expected to blow a $6-billion hole in the upcoming 2013-14 provincial budget.
Redford's comments came two days after the city and Oilers owner Daryl Katz agreed on a framework deal to build a $480-million downtown arena for the NHL franchise.
Once surrounding infrastructure is added in, the cost will be $601 million, paid for by the city, the Oilers, a ticket tax, with another $107 million hopefully coming from the province and $7 million from the federal government.
Alberta NDP Leader Brian Mason said while the gaming idea is kaput, the game is still on given that Katz, his family, and business associates donated $430,000 to Redford's Progressive Conservative Party in last spring's election.
"Given the fact that (Katz) donated $430,000 to them in the last campaign and saved their neck, that's one promise I expect (Redford) to actually keep," said Mason.
Alberta's chief electoral officer is investigating whether Katz violated the maximum individual donation limit of $30,000.
Earlier this month, Wildrose Leader Danielle Smith suggested a keno lottery to fund the arena and keep tax dollars for other priorities.
Redford didn't act on that, and Smith said there's nothing to be done.
"I think we did our part, looking at various options and putting forward a responsible proposal," said Smith.
"It's disappointing that (Redford) is not going to consider it."
Construction is slated to begin in the fall and the arena should be ready for pro hockey by 2016. The rink is a futuristic design of glass walls and wavy horizontal lines.
Edmonton taxpayers are to pay $219 million toward the 18,559-seat facility. The Oilers' share will be $143 million. Another $125 million will come from a ticket tax.
Prime Minister Stephen Harper's government has said there's no money for projects like arenas for pro hockey teams.
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