Saputo's new offer is $9 per share in Australian currency, making Warrnambool Cheese and Butter's total equity worth about A$499 million, or about C$487 million, not counting assumed debt.
Saputo's previous offer was A$8 per share of Warrnambool but rival Murray Goulburn Co-operative announced earlier this week that it would offer A$9 per share.
A combination of Murray Goulburn and Warrnambool would have 41 per cent of the Australian market while a deal with Saputo would give the Canadian company about 10 per cent.
Saputo says its offer will be unconditional and superior to all other proposals, including the one from Murray Goulburn or another from Bega Cheese Ltd., which has offered about A$8.675.
The Montreal-based company had previously said its offer depended on Saputo getting at least 50.1 per cent of Warrnambool equity. It still is offering to buy 100 per cent of the Australian company but dropping the minimum threshold means it would accept a minority stake.
Saputo says Murray Goulburn's offer is "highly conditional" because it is subject to receiving approval from Australian competition authorities.
However, Saputo's task is complicated by the fact that Murray Goulburn and Bega already own sizeable stakes in the target company and another large chunk of Warrnambool is owned by a third company that's already in the Australian market.
As of late October, a total of about 46 per cent of Warrnambool was owned by either Murray Goulburn (18 per cent), Bega (18 per cent) or Lion (10 per cent), a Japanese company.
RBC Dominion analyst Irene Nattel said in a research note that it remains to be seen whether Saputo will be able to claim the prize, which she says is strategically important for the Canadian company.
"Given ongoing uncertainty around eventual outcome, we are leaving our F15 (fiscal 2015) forecasts unchanged, but we note that a successful acquisition of WCB would enhance SAP's growth outlook," Nattel wrote.
"Strategic rationale for the transaction remains clear: WCB would provide SAP with opportunities to capitalize on growing global demand for dairy solids.
"Australia is currently the third-largest exporter of milk products globally (after the EU and New Zealand), with approximately 10 per cent share of market."
Additionally, Australia is one of the three low-cost milk producers globally. New Zealand is another of the three and the third is Argentina, where Saputo is the third-largest milk producer.
— by David Paddon in Toronto