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The company said it had made a non-binding indicative offer to acquire a 75.1 per cent interest in MVM, based on an enterprise value of about $385 million.
MVM had now agreed to provide a2 Milk period of exclusivity to conduct due diligence and documentation.
The exclusivity arrangements are supported by MVM's majority shareholder, China Animal Husbandry Group (CAHG), which would retain a 24.9 per cent interest.
CAHG is a wholly owned subsidiary of China National Agriculture Development Group, which is also the parent company of a2 Milk's strategic partner in China, CSFA Holdings Shanghai (China State Farm).
Chief executive Geoff Babidge said a2 Milk had been assessing participation in manufacturing capacity and capability because of the increasing scale of its infant nutrition business.
"The potential investment in Mataura Valley Milk's recently commissioned facility, alongside China Animal Husbandry Group, aligns with this strategic objective as we look to complement and build upon our current strategic relationships with Synlait Milk and Fonterra Co-operative Group, which remain in place," he said.
A2 Milk plans to invest further to establish blending and canning capacity at Mataura's facility to support setting up a fully integrated manufacturing plant for infant nutrition.
Discussions with MVM were "ongoing and remain incomplete".
Any transaction that results from the current discussions is expected to be settled towards the end of a2 Milk's cash reserves.
At its annual result this week, a2 Milk said its cash balance was $854m.
The move appeared to have the blessing of Synlait Milk, which exclusively makes formula for a2 Milk and which is part owned by the company.
Synlait said it had a "long-standing, strong and complementary partnership" with a2 Milk.
"It is a partnership that continues to strengthen as both companies grow together," Synlait said.
"Synlait is well positioned to continue to support and enable a2 Milk's growth aspirations via its highly integrated infant formula manufacturing capabilities that meet the high standards in China - the world's largest infant nutrition market," it said.