Southern - New Zealand's biggest institutional dairy fund and 50 per cent owner of upmarket dairy brand Lewis Road Creamery - was seeking more information on the offer before it made its decision, she said.
Landcorp, which operates under "Pāmu" brand name, has about 4.5 per cent of Westland.
"Pāmu will be carefully assessing what is in the best interests of Westland and dairy farming on the West Coast, as we work to determine how we will vote on this important decision for the future of Westland," spokesman Simon King said.
"We have not yet received the full details of the offer and it would therefore be inappropriate to comment further."
The average Westland Milk farmer will walk away with just under a million dollars if the offer is successful.
As part of the deal, Yili will at least match Fonterra's farmgate milk price for the next 10 years, starting from August 1.
Westland chair Pete Morrison said the main reason for the deal was Westland's inability to deliver a competitive milk payout in recent years.
At Fonterra's interim result this week, chairman John Monaghan confirmed that Fonterra had been in talks with Westland when it first revealed that it was looking at changes to its capital structure.
"Firstly, we are sorry to see the demise of another New Zealand co-op and of course supplier shareholders are welcome back to our co-op," he said.
As far as the 10-year clause went, Monaghan said: "Ten years can go very quickly for what is an inter-generational business, and it's what happens beyond that that becomes important," he said.
The proposed sale is to Hongkong Jingang Trade Holding Co, a unit of Inner Mongolia Yili Industrial Group.
Southern Pasture's holding stems from a deal signed early last year that involved Soutner supplying Westland with 4 million kilograms of milksolids a year.
Westland's profit for the year to July 2018 came to just $560,000, down from $1.5 million a year earlier, and the last annual report puts its total interest bearing borrowings at $232.8 million.
Yili is the largest dairy producer in China and Asia and has a strategy to grow both its domestic and global businesses.
Westland is New Zealand's second biggest dairy co-op after Fonterra, but with just 429 farmer-shareholders, it is dwarfed by Fonterra's 10,000 or so.