Bangladesh are in New Zealand to play one Twenty20 match, three one-day internationals and one test.
Tuffey said playing well and winning every match against Bangladesh would set the Black Caps up for the Australians who will tour next month.
"We do want to whitewash them in all forms of the games especially moving forward against Australia next month," Tuffey told RadioLive.
However, Bangladesh coach Jamie Siddons said his side are a lot further developed than the one that last toured New Zealand in 2007-08.
"We are still a young side but they are starting to show real signs we are improving," he said, pointing to the fact the three batsman had made centuries against India recently.
"In the one-dayers against India, 250 was our last score and 296 was our best score - these are great scores in our conditions over there.
"In the test against India, we had three different guys make 100s and five bowlers taking five-fors (five wickets or more in an innings).
"We also saw (skipper and left arm spinner) Shakib (Al Hasan) continuing his form with another five-for so that's really great signs for us."
Australian Siddons, who had his contract extended to the 2011 World Cup after Bangladesh won their first test series overseas in the West Indies last year, confirmed that key bowler Mashrafe Mortaza would not make the trip to New Zealand.
"At this stage, he will not be coming over. He picked up a bit of a fever and hadn't done a lot of work. It probably set him back another week so it is not worth bringing him in."
He made light of Mark Greatbatch's appointment as New Zealand.
"I don't think it makes them vulnerable - they don't seem to be confused and they are all very happy with the new coach.
"They have had Dan (Vettori) there the whole time who is probably their general anyway.
"There may be a little bit of nerves so if we can play well, we can put them under some pressure."
Siddons said limiting the potential for damage by Vettori and Ross Taylor would be uppermost in his side's minds.
"Daniel has picked up wickets at the wrong times for us in test or one-dayers.
"He was the only thing stopping us from cleaning up New Zealand over there in Bangladesh last time. If we can get on top of him and minimise his damage then I think we will go all right.
"Taylor is a good hitter - we'll probably try and not bowl full tosses and half-trackers at him . . . . "
Tuffey deflected any suggestion that the Black Caps was under more pressure to perform following the controversial departure of former coach Andy Moles four months ago after he lost the confidence of senior players.
"I don't think there is any more pressure to perform than usual," Tuffey said. "It's going to be a tough series and we want to play well."
The tour opens with a Twenty20 match on Wednesday at Hamiilton.
