"The Government have come on board, they've been with us the whole way. This is the reason why it'll be pumped through pretty quick.''
The plan would take recovery workers as far as the rockfall in the mine, but it was not known whether the men's bodies were further down than that.
"We don't know this and it's all high speculation. Everyone says we may get close for the families, and I've seen [Prime Minister John Key] saying that it might be heartbreaking if we get down to the rockfall and can't get any further. No one is positive of what is going to happen when we get down there, but we have to try,'' Mr Monk said.
Labour Minister Simon Bridges told 3 News he would not be stalling on pushing the plan through.
"I won't muck around, I will move on that with real haste and will get that to Cabinet,'' he said.
Prime Minister John Key has pledged $10 million for the re-entry if the plan goes through.
West Coast Labour MP Damien O'Connor said the plans for re-entry were "welcome news'' for the Pike families.
"This is a long-awaited decision for the families and it will hopefully offer some emotional compensation for the huge loss they suffered,'' he said.
He also called on the Government to "proceed quickly'' if approval was granted this month.