Victory will secure the All Blacks' first clean sweep of the home nations since 1978 when Graham Mourie's legendary side became the first to achieve the feat.
The 24-year-old lock accepts his side are strong favourites to defeat the Scots at the weekend but anticipates a fierce resistance in Edinburgh.
Williams said: "We know the Scottish are very passionate and they will like the fact they are underdogs. They really relish big challenges.
"We are expecting a huge performance from them and nothing shy of what any nation plays like at home.
"They will want to do the best they can against us and to do it to the very best of their ability."
New Zealand coaches Graham Henry, Steve Hansen and Wayne Smith have already announced 13 changes to the side which defeated England 23-19 at Twickenham last Saturday.
Captain Tana Umaga and lock forward Chris Jack are the only players to have retained a place in the starting line-up.
But Williams, speaking at a civic reception in Glasgow to mark the first visit of the All Blacks to city in 1905, accepted victory would provide the players with a special moment.
He said: "It will be a great occasion for the team and we want to finish our tour on a high note.
"The Grand Slam is definitely in our minds now but really it is just about rounding it all off and we are relishing it.
"We haven't been thinking about it too much at all during the tour.
"It has been more about going game-by-game and moving towards achieving more of the things this team is capable of.
"I don't think we have been a smooth as we can be because we have not had as much game-time as we would have wanted.
"But the purpose of this tour was to give everyone experience and we have gone a long way towards doing that."
New Zealand team to face Scotland at Murrayfield:
I Toeava; R Gear, C Smith, T Umaga (capt), J Rokocoko; N Evans, P Weepu, S Taumoepeau, A Oliver, J Afoa, C Jack, J Ryan, A MacDonald, S Lauaki; R McCaw.
Substitutes: A Hore, N Tialata, J Eaton, M Tuiali'i, J Cowan, L MacDonald, M Nonu.