White told Tony Veitch on Radio Sport today that the upcoming tests series in Australia will certainly air on Sky but couldn't confirm if any other away fixtures next season would be screened in New Zealand.
The Black Caps have the Twenty20 World Cup in India in March-April and a test series in South Africa.
"Unfortunately I can't give any assurances. This is an open market and it's a property we don't own," White said.
"What I can say is that behind the scenes we'll be talking and trying to influence in trying to ensure our team is on TV. I think it's important to point out this is the first time in 13 years that this has happened. I'm hopeful that this is just a one-off."
White was very grateful that Cricket South Africa had stepped in to provide coverage free of charge.
"It's been frustrating for the fans and everyone concerned really that they haven't been able to watch the first few games. Thank you to Cricket South Africa for being able to do that. We're very pleased," he said.
Cricket South Africa chief executive Haroon Lorgat said in a press release that there would be no commercial gain from the live streaming and that media reports failed to 'accurately report' the negotiation process with Sky.
"With New Zealand cricket fans top of our minds, we were determined to provide them with live action of two top teams and this will now happen through live web streaming," Lorgat said.
"There will be no commercial gain for us streaming live but at the same time it presents us with an exciting opportunity to enter the world of live streaming of our events for the very first time.
"I must take this opportunity to express disappointment at not having concluded a deal earlier with Sky NZ and to later media reports which failed to accurately report the state of affairs.
"I must also take this opportunity to thank our host broadcaster, SuperSport, and the other partners including IMG who worked around the clock to make this possible for fans in New Zealand." concluded Lorgat.
The second ODI begins 8pm tonight in Potchefstroom. Radio Sport will also provide commentary from 8pm.