The Montreal-based dairy (TSX:SAP), which already controls just under 21.4 per cent of Warrnambool's stock, said the new deadline to tender to the offer is Jan. 22.
The multi-faceted bid had been set to expire on Friday.
Saputo described the bid as its "last and final offer" and said "there will be no further extension to the offer period."
Saputo has bid AU$9.20 per Warrnambool share if it gets a simple majority, AU$9.40 per share if it gets 75 per cent of the total and AU$9.60 per share if it gets at least 90 per cent of WCB's stock.
A rival bidder, Australia's Murray Goulburn, has offered AU$9.50 per share, conditional on it securing a majority of WCB shares and winning support from the Australian Competition Tribunal. The tribunal is holding hearings on the issue in February.
Murray Goulburn, with 17.7 per cent of Warrnambool's stock, is the company third- biggest stakeholder after Saputo and Bega Cheese, another Australian company which controls 18.8 per cent of WCB shares.
Word on a possible extension of Saputo's bid was first reported in an Australian newspaper, but that had been downplayed earlier Thursday by a Saputo spokeswoman.
"You can be sure that if there was such an announcement, we would make it available on the Australian Stock Exchange and on (the) TSX," Sandy Vassiadis wrote in an email.
The Australian newspaper said Saputo was running the risk of angering the country's takeovers panel for a second time by waiting until the last minute to extend its offer.
Saputo increased its bid in mid-December after the regulator criticized a decision by Saputo and Warrnambool to remove a special dividend in an earlier bid, which it said created "confusion and disruption" to the market for Warrnambool shares.
Meanwhile, the Australian Competition and Consumer Commission, which is assisting the takeover tribunal, has reiterated its concerns about Murray Goulburn's submission.
''The ACCC considers that a there is potential for the proposed acquisition to have the effect of lessening competition in the acquisition of raw milk,'' the commission said in a 76-page report, which had parts blacked out.
The agency made similar comments when Murray Goulburn tried to acquire Warrnambool in 2010.
Saputo's shares closed up 10 cents Thursday at C$49.01 on the Toronto Stock Exchange.