Mr Kokshoorn said Mr Key had indicated to him that the Government would contribute towards the trust, which he expected would have money from different parties totalling $12 million to $15 million for the recovery operations.
"We need to get something firmly in place that will keep the recovery going."
A spokeswoman for Mr Key said: "The Prime Minister has agreed to meet with Mr Kokshoorn, at his request. It is premature for the Prime Minister to comment about the issues for discussion or likely outcome of the meeting at this stage.
"The Prime Minister appreciates the interest of the West Coast and the families in making progress on recovering the bodies of the deceased [workers] if this proves at all possible".
Receiver John Fisk said he was open to ideas about how best to operate a trust.
There had been discussion with the potential new mine owner about setting money aside from the sale to put into a trust.
"The suggestion at the moment is they might pay X for the [mine] assets, and Y would be put aside in a trust to be used for that recovery exercise. I can't really comment on numbers at the moment. A lot will come down to negotiation with whoever the stakeholders are that are going to contribute to it."
The cost of recovering any remains was still "very much an unknown quantity".