"Inquiries were made at a number of venues in Auckland for a gig at [early June] but it now looks like all bets are off."
The singer's latest show has an extended stage that uses a lot of space on the floor of an arena, which it is thought would push ticket prices up to unaffordable levels as there would be less room for the audience.
The source added: "There is always the chance that Prince could come over to New Zealand from Australia and put on a few last-minute small club gigs, but that is now looking like a real long-shot."