Others who have announced bids for the mayoralty include former Green Party chief of staff Tory Whanau, Barbara McKenzie, and Ray Chung.
Asked whether Foster or Eagle would get her vote, Prendergast said she wanted to see what their vision was for broken water pipes, getting the city's transport network moving, and affordable housing.
"It's not safe. I don't feel safe anymore walking home at night in parts of the city.
"I want it to be the way it used to be - bubbly and bright. People that respected heritage, respected urban development, respected urban design. Cosmopolitan. Cafes, restaurants, helping the hospitality sector, helping the retail sector."
Prendergast said it was important contenders had a team around them to drive their vision because they couldn't do it on their own.
"So, has this person got the leadership qualities... to do deals, to cut deals and get on with making our city great again?"
Voters would also be considering how much of the council in-fighting experienced this term was the mayor's responsibility, she said.
It's understood if Eagle does run, it will likely be as an independent endorsed by the Labour Party.
Prendergast said she suspected Eagle would have Labour's support, although she described him as being centrist in his politics.
"He has worked in council before and he's been a city councillor. So he certainly understands the business of local government. He certainly will have contacts in central government to get the support the city needs from central government."
Prendergast said she was "positive" Foster would run, the question was more whether he would also run in his ward as opposed to mayor or nothing.
She thought Foster had a chance because a lot of local body elections was about name recognition.