On Wednesday, Oracle Team USA released the rules and structure of the America's Cup but did not reveal where the event will be held.
At the time, Team NZ chief executive Grant Dalton said the team "can't raise real money" without knowing the venue.
Mr Joyce said any decision on further government funding would depend "on the attitude of the other players".
"There's a big yachting community in New Zealand who are keen to see a challenge. I think it would be a good idea for some of them to step up at this point.
"And of course there's a bunch of other sponsors who, as I understand it, indicated to Team New Zealand that they're very keen to keep participating. So they should probably step up a bit now as well."
Mr Joyce met Team NZ last week before the protocol for the next Cup was released, but would not say how much money the team needed.
"They didn't ask for a specific amount, but we know that the $5 million that they got from us in November/December last year, that's about three to seven months, so they would need something similar from their sponsors over the next period."
Mr Joyce said he believed the Cup was "still a great thing for New Zealand in terms of marketing opportunities".
"I think there's some strong profile opportunities in that for New Zealand, and therefore it makes sense for us to be involved in some way.
"But actually, look, it's never going to happen without all the other sponsors. There's no way that this is a government-funded challenge."
The contest has a US$2 million entry fee, due by August 8.
Cup challenges
• Steven Joyce has not ruled out putting extra government funding into a new America's Cup challenge.
• Oracle Team USA have released the rules and structure of the Cup but did not reveal where the event will be held.
• The contest has a US$2 million entry fee, due by August 8.