Nigeria are "destined for something special" at the Women's World Cup, their coach Randy Waldrum has said, after reaching the last 16 and a likely clash with England.

The Super Falcons confounded expectations by beating co-hosts Australia 3-2 on the way to progressing unbeaten from one of the toughest groups at the tournament.

A 0-0 stalemate against Olympic champions Canada, the stunning Australia win and then another goalless draw on Monday against already eliminated Ireland put Nigeria into the knockout stage.

England need only a point against China on Tuesday to top Group D, which would set them up to meet 40th-ranked Nigeria on Monday.

"We were 20 spots below all the other teams in the group -- at a minimum -- in the rankings," said Waldrum, who was in open conflict with Nigerian football chiefs on the eve of the World Cup over pay and funding. 

"It's testament to these players, they have not been given everything that other federations have but given the opportunity to get here they have put everything into it," the 66-year-old Texan added.

"I just feel like they all believe we are destined for something special at this World Cup. Our journey is not over and we will be very, very well prepared for whoever we play next week.

"I give the credit to the players. It is an amazing group of women."

Nigeria have been to all nine Women's World Cups since the tournament began in 1991 but this is only the third time they have reached the knockout phase. 

It is the first time they have gone through the group phase unbeaten.

They were especially impressive in coming back from a goal down to beat Australia, when they were lethal on the break.

Waldrum was branded "a loudmouth" by the Nigerian Football Federation after speaking out before the tournament.

Asked if his team's performances had rebuffed that criticism on his behalf, Waldrum preferred to talk about his players.

"I can't control how people feel about me," he said.

"All I can do is do the best job I can and I hope we have proved some people who did not believe in us wrong.

"The credit goes to these young women for believing in what I am trying to get them to do. I could not have asked more from them."

Having got out of a tough group, Waldrum said his team feared nobody, not even England.

"Bring on the European champions, why not?

"Don't count us out against England, we will be prepared."