Billy Vunipola has warned the All Blacks that England are hunting down their world No1 spot.
Having clinched the Six Nations title with a 61-21 mauling of Scotland, England will surpass New Zealand's world record 18-match unbeaten run and secure the first back-to-back Grand Slam triumph in Six Nations history with victory against Ireland in Dublin on Sunday morning NZ time.
And Vunipola said: "We know we're not No1 yet, but we want to do things within our power to show we're serious about this goal."
All Blacks coach Steve Hansen sent a message of congratulations to "champ" Eddie Jones on Sunday.
And England No8 Vunipola made it clear he wants to knock New Zealand off their perch.
He said: "Eddie pushed us massively to a goal that everyone laughed off at the end of the World Cup but now it's realistic. It's about being relentless with everything.
"Do we want to make the next step or start again from the bottom?"
Jones claimed his players will achieve "greatness" if they become the first nation in the competition's six-team history to secure back-to-back Grand Slams.
Victory would maintain the head coach's perfect run since taking charge.
Hansen claimed he would relish a showdown with England, although that doesn't look like it will happen this year despite the All Blacks being yet to confirm their final international on their end-of-season tour to the Northern Hemisphere.
"Being All Blacks coach I'd like to think we would win," Hansen told the BBC. "Eddie being England coach would like to think they would. Hopefully the game lives up to the hype."
There is no fixture scheduled between the countries until November 2018 but Hansen added: "When the time comes it will be a cracker. It's something rugby people want to see. Right now they are the team that's out there doing it".
England returned to training overnight with Jones sweating over Elliot Daly's fitness after suffering a head injury against Scotland.
First-five George Ford said: "We are trying to go and create some history and memories.When you win the Six Nations and the Grand Slam like we did last year, other teams will be more prepared. We want to go one better and get that Grand Slam again."