The former All Black died of a suspected heart attack last week in Perth, where he had been living and working as a forklift driver. He was survived by six children.
Berryman was meant to spend the night at Perth's Wanneroo Rugby Club tonight, where he coached kids' rugby, but the venue had to be changed because of the sheer number of people planning to attend.
Family and friends are now viewing his body at the larger Landsdale Farm - about 500 metres from the club - and many were planning to stay overnight.
The formal tangi will be held at Pinnaroo Memorial Grounds on Wednesday and arrangements are being made to live-stream it to New Zealand.
Club president Francis Williams said the huge numbers showed how many lives Berryman had touched.
"It takes you back a bit, the magnitude of the outpour," he said.
"You meet the man, and he's very humble, very modest, and you realise when he's passed the amount of lives that he's touched and the influence that he has is far and well beyond that."
Berryman represented the Crusaders, Chiefs and Blues in Super Rugby and was a stalwart of the Northland NPC team before moving overseas.
He became involved with Wanneroo about five years ago, when his son Terrell started playing for the junior team, and many of his family members were also involved in the club.
The club put on a fundraiser at junior games on Friday night and has created a new trophy - the Norm Berryman Cup - which will kick off between Wanneroo and Kalamunda on August 1.
A Give a Little page set up to raise money to support his family has reached more than $14,600 so far.
Mr Williams said the club was doing what it could for the family of "larger than life" Berryman as they grieved.
"For the family it's only a small amount that can't compensate for the loss. His young kids, we'll always give our support to them and try and help them out wherever we can.
"That's just the rugby community. They're always going to try and look after them."
- By Lauren Priestley and Eli Orzessek of NZME. News Service
