The Greens are polling at about 5 or 6per cent, right on the threshold for getting back into parliament.
But regardless of that, White said she wouldn't be making way for Swarbrick in Auckland Central.
"I actually think the Greens will be fine, they've got a solid base and obviously Chloe is way up on that list, so people will firmly expect to see Chloe in parliament."
Asked what she would say to people who pointed out Swarbrick's higher profile and name recognition, White said: "I'd ask them whether they're looking for a celebrity or someone to do this job very seriously."
At a campaign event in Auckland last night, Labour's national campaign manager Hayden Munro told the crowd the party could not afford to split the progressive vote in the seat.
In 2017, the combined progressive vote in Auckland Central was just over 50 per cent.
"If that vote is split, a National candidate can come through the middle," he said.
The event was also attended by Justice Minister Andrew Little and Labour's Mount Roskill MP Michael Wood.