However, they also said she could be motivated by recent events to return.
Street criticised Little on social media this month over his recruitment of controversial broadcaster Willie Jackson and his promise to give Jackson a high list placing.
In a Facebook post, she praised Labour's new Nelson candidate, Rachel Boyack, for securing her nomination on merit and "not through shoulder-tapping or list-jigging" - a clear reference to Little and Jackson.
She went on to list several of Labour's women candidates and said they had "no safe seat or guaranteed high list placing".
Street is a vocal advocate for legalising assisted dying in New Zealand and a select committee is currently considering her petition on the issue.
When Little became leader in 2014, he insisted that Street's former private member's bill on legalising euthanasia - now in the name of Labour MP Iain Lees-Galloway - should not return to the ballot because it was not a priority for the party.
If Street steps aside, Mackey is next on the list. Mackey, now working at the Wellington City Council, said yesterday she did not want to return to Parliament.
"I've got a job I really enjoy and I've discovered life after Parliament. I have weekends and evenings and I'm not flying everywhere four or five times a week."
Auckland-based, Chinese-born former MP Raymond Huo comes after Mackey. Little is understood to want Huo to return to Parliament to help Labour attract Chinese voters.
Huo would not comment yesterday.
Ardern is up against Green Party MP Julie Anne Genter, The Opportunities Party's Geoff Simmons and 11 other candidates in the byelection on Saturday, February 25.
Nearly 2000 people have cast advance votes in the eight days since voting opened, slightly behind advance voting numbers at the same period in the general election.