However, he said it was "very unlikely" Auckland ratepayers would be asked to foot the bill for cost overruns.
SkyCity and the Government agreed a deal in July 2013 for the casino operator to spend $402 million to build and operate the New Zealand International Convention Centre in exchange for legislation allowing the company to operate additional gambling tables and machines and extending its gambling licence to 2040.
The law was changed in late 2013, but in December last year, SkyCity managing director Nigel Morrison said cost over-runs and "design improvements" had seen the bill blow out to between $470 million and $530 million.
Mr Morrison told financial analysts SkyCity was unwilling to contribute more than $10 million to the gap without compensation for his shareholders, and floated the possibility of financial support from central or local government (report continues after interactive).
Interactive: Slide the rule to see how the convention will affect the city skyline
Mr Key today told reporters he could not rule out taxpayer money being used to meet some of the cost overrun, but negotiations were ongoing and nothing had been taken off the table.
"In a nutshell, the Government has an agreement with them [SkyCity]. It could make them meet that agreement but the escalation in prices to build the convention centre, which is bigger than was proposed and flasher than was proposed, means there is a hole.
"So there are a couple of options. Option one would be to say to Sky City, 'Build the convention centre exactly at the price that we all agreed, on the conditions of the deal that we agreed', but it would be smaller I think than we had hoped and less attractive.
"Or the second option is to see if there's any way of filling that hole and to identify how big that hole is, and that's the process we're going through."
Auckland Mayor Len Brown said he could not see a situation where ratepayer money would be committed to the SkyCity deal.
On Mr Key's "eyesore" comments, Mr Brown said it would be unhelpful for him to comment from the sidelines.
"But I have consistently encouraged SkyCity to take the opportunity to create a truly iconic building for Auckland.
"I know the commitment that both the government and SkyCity have to delivering a high quality, iconic national facility. However the funding discussions end up, I have full confidence that is what we will end up with."
SkyCity chief executive Nigel Morrison said in a statement that constructive discussions with the Government were continuing.
"SkyCity remains committed to building, developing and operating the [convention centre] and we are optimistic we will come to a solution.
"SkyCity looks forward to progressing the [convention centre] project, which will provide substantial economic benefits for Auckland and New Zealand."
Promise to New Zealanders
Economic Development Minister Steven Joyce last year raised the prospect of the Auckland Council helping fund the project, a suggestion that was angrily rejected by many councillors.
Mr Key today backed away from that option but asked if he could rule out taxpayer money being used, he said he could not.
"What I can say is that we are working very closely with SkyCity...to try and see if a deal can be completed. But as we always said, the deal was never a done deal until ultimately everything was ticked off."
Labour leader Andrew Little said the promise made to New Zealanders was clear - that the convention centre would be constructed for free.
"They promised us they had got the deal of the century...now it looks like taxpayers are going to be asked to pony up $140 million. They have broken the promise. I would like to see what a $402 million eye sore looks like...taxpayer money should not go in to a convention centre that we were promised for free."
Asked if the Government could walk away from the deal, Mr Joyce, who is leading the negotiations, said it was always an option, "but there's nobody else volunteering to stump up with $402 million to get us back to the same point".
Mr Joyce said it was not possible to structure the initial deal in such a way that made clear any cost over-runs would be met by SkyCity as at the time it was a case of concept drawings and "nobody would sign-up to a final fixed price".
He could not say when a decision would be made on what to do about the convention centre.
"I particularly don't put dates on these things because that hands negotiating coin to the other side, and I'd rather that we just worked our way through it."
