Despite the fact the Scots have a dismal record against the world champions, and have never beaten them, the game is on course for a sell-out.
The sides last met two years ago at the same venue and the All Blacks romped to a 49-3 victory.
Only once in the last six meetings has the world's No.1-ranked team failed to put over 30 points on the board, when they ran out 29-10 victors seven years ago.
But Lineen believes that if Andy Robinson's men follow the recent ultra-aggressive performance of Australia, who claimed a draw against the All Blacks in Bledisloe Cup action, they can compete.
He said: "Andy has picked a strong side. We have a big powerful pack that will compete at the lineout well and also, I believe, in the scrum.
"If you look at the recent game between Australia and New Zealand then the Wallabies really tore into New Zealand from the kick-off and that has to be the template for Scotland on Sunday.
"It is going to be about bringing our A-game to the table and producing it for 80 minutes. We may be massive underdogs but, at the same time, this is a massive opportunity for the Scotland side.
"From what I have heard, the All Blacks are going to use the game with us and then their next one with Italy to test out a few combinations and that could present an opportunity for us to ruffle a few feathers.
"But it is going to take a huge performance and, if Scotland can stay within 12 points, that will be a fantastic result."
However, the Grand Slam-winning centre has pinpointed an area of concern which he believes is as strong as any head coach Robinson could have picked.
Lineen said: "At centre we are going to need a very big game from both Nick De Luca and Matt Scott. I think they can expect a lot of powerful runners coming their way on Sunday.
"But we will also have to defend well on the flanks as the All Blacks love to play with width."
Lineen believes some of his old Glasgow Warriors' charges can make a significant contribution.
"I think we have a powerful second row in Richie Gray and Jim Hamilton, who will really compete at the lineout," he said.
"It is a big plus that Richie has made it back from his ankle injury and to have Al Kellock coming off the bench will mean we should be more than competitive in there and that will be vital.
"Also in the front row, Ryan Grant will be looking to build on his heroics Down Under in the summer and I like the look of the Scotland scrum.
"At full-back Stuart Hogg is the type of confident young boy who will relish taking on the world champions and I think he has the skillset to hurt them at 15. This is an opportunity for every one of the lads to test themselves."