Captain Brendon McCullum isn't content with New Zealand's world ranking of third, believing top spot is a realistic target for his team on the rise.
The Black Caps take an enviable recent record into their two-Test series against fifth-ranked England starting at Lord's on Thursday.
However, despite having won four and drawn two of their past six Test series, McCullum believes his team have more to offer.
Surpassing leaders South Africa and Australia as cricket's top-rated team isn't the far-fetched goal that many may believe, McCullum said.
"You want to get to the top and when you get to the top you want to stay at the top and you want to push the game forward," McCullum said.
"It's going to take a lot of hard work because there are a lot of good teams around the world. If we can perform well here it would be another stride for us."
The Black Caps are also ranked third in one-day cricket on the back of their run to the World Cup final.
McCullum wants his team to keep riding the momentum generated at that tournament but also be aware of Test fundamentals and remember what their shortcomings were when they beat Sri Lanka 2-0 at home five months ago.
"We have made some progress but we are only No.3 in the world," he said.
"We still have some improvements to make. We still have some respect to earn around the world."
McCullum says the Lord's pitch appears drier than he expected but should still be helpful for swing bowling if cloud conditions suit.
Conditions on the day will determine whether pace bowler Matt Henry makes his Test debut as the third seamer or if the selectors stay with incumbent Doug Bracewell or even return to Neil Wagner.
In-form opener Martin Guptill is poised to play his first Test in two years, joining Tom Latham at the top of the order in place of left-hander Hamish Rutherford.
WORLD RANKINGS
1.South Africa (130 Rating)
2. Australia (108)
3. New Zealand (99)
4. India (99)
5. England (97)
6. Pakistan (97)
7. Sri Lanka (96)
8. West Indies (84)
9.Bangladesh (39)
10. Zimbabwe (5).
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