The Australian media has been rife with speculation as to who might be interested in Murray Goulburn which, like Fonterra, is a co-operative.
Several players have been mentioned as possible suitors, from China's Yili, to Australia's Parmalat to the French dairy company Lactalis.
Fonterra's chief executive Theo Spierings said on Monday that Fonterra is in a strong position to pick up distressed dairy assets around the world after the price volatility of the last few years had left some in bad financial shape.
Earlier this year, Fonterra was in talks with the financially troubled Argentinian dairy company Sancor, which did not materialise into a deal.
Fonterra, historically the second biggest dairy company in Australia, has been gaining a greater share of milk production there while Murray Goulburn's share has slumped.
The Australian Competition and Consumer Commission's agriculture commissioner, Mick Keogh, said the commission was watching the situation.
"As far as we are aware there are up to a half a dozen different bids either for part or the entirety of Murray Goulburn," Keogh told the ABC.
"If we're talking hypothetically about two of the largest players proposing to merge, yes, you would think that would have a likely affect on competition in the dairy industry," he said.
Units in Fonterra last traded on the NZX at $6.24, up 3c since Tuesday's close.