Buoyed by narrow losses to the unbeaten Australians in their last two triangular series one-day internationals, Fleming said the gulf between the teams was not as great as their recent head-to-head record suggested.
Australia have won 19 of their past 21 games against New Zealand, but the home side prevailed by just two wickets in Adelaide last week after the Black Caps paid a hefty price for several dropped catches.
On Sunday, Australia made a record 343 for five at the WACA but the Kiwis fell just eight runs in short in finishing on 335 for five.
Speaking here after Sunday's game, Fleming said the desire to beat their arch-rivals, along with the confidence they can do it, was growing with each narrow loss.
"There is a massive desire to beat them and it is probably born from believing we are not too far away," he said here after Sunday's game.
"Statistically, we are a long way away, something like 21 (losses) and two (wins) or 26 and five, but we think we are pretty close."
The Australians are short-priced favourites for the upcoming World Cup in the Caribbean, which is just six weeks away.
New Zealand's highly competitive form bodes well for their chances in the tournament and Fleming said their batting line-up was now looking more balanced, with Jacob Oram slotting back in at No.6 and Brendon McCullum dropping down to No.7 after being tried as an opener.
Lou Vincent was recalled to the top of the order on Sunday because of Nathan Astle's retirement and made 66, Fleming appears to slowly be regaining form and Scott Styris should soon be back from injury and slot into the middle order.
"To get 330-odd chasing a big score is a positive we will take out of it," Fleming said of Sunday's game.
Dropped catches have cost New Zealand dearly in their last two losses to Australia, but Fleming dismissed suggestions his players were feeling the pressure to beat the world's best side.
Fleming said it was more that the Australians highlight any fielding errors.
"Australia makes you pay -- other teams don't make you pay as much," he said.