"At this point it looks like they will get here during the first innings," said race director Jack Lloyd.
"There is an outside chance they will get here by the morning, but it's likely to be more like Saturday afternoon."
Despite spending three weeks at sea, existing on freeze-dried food and minimal sleep, Swete, a keen cricket fan, is prepared to leap straight off a boat and head to Eden Park if it means catching the Black Caps in action against their traditional foes.
"If we get there on time I will be jumping in a taxi straight from the Viaduct and forgoing my beloved post-Volvo-leg shower to watch the game," Swete said.
"So, if you're going to the game you could potentially be sitting next to someone who has not showered for 21 days."
The 31-year-old helmsman's enthusiasm for cricket is not shared by most of his crewmates.
Nevertheless, Swete has been trying to school them on the nuances of the sport.
"The two Europeans have never heard of the game," Swete said.
"And the four Americans who forced us to adopt NFL teams and learn about the game have just started showing interest - even if they are just drawing parallels to the game of baseball."
However, Swete and his Kiwi crewmate Ryan Houston at least have one Australian on board they can bait, navigator Will Oxley.
"[Will] is a massive cricket fan so there is plenty of banter.
"Will is not a betting man but Housty and I are very confident we can beat the Aussies at Eden Park so are still baiting him for a bet," said Swete.
This weekend will be the second time Swete has experienced an Auckland homecoming in the round-the-world yacht race.
He also crewed for Mike Sanderson's Team Sanya in the 2011/12 edition of the race.
Both he and Houston are graduates of the Royal New Zealand Yacht Squadron's youth programme.
Early yesterday evening, the Volvo fleet had just skirted New Caledonia, and was 800 nautical miles north of Auckland.
Volvo Ocean Race
• Leg 4 - Sanya-Auckland
• 5264 nautical miles
• ETA: Saturday afternoon.
- additional reporting Vaimoana Tapaleao