The offer was made by TGP and follows a bid from US private equity giants KKR and Rhone Group earlier this month.
Treasury previously rejected a £1.7 billion takeover bid from KKR in May.
Market analyst Evan Lucas of IG Markets said: “It has been closely watched by private equity firms since it was spun out from Fosters group in 2011.
“Drinking habits globally have also seen wine moving up the list in liquor consumption, while brands such as Penfolds and Seppelt demand premium on the global stage, and that is where private equity firms see value.”
Treasury said: “The board has concluded that it is in the interests of its shareholders to engage further with this private equity investor. Therefore, subject to the negotiation of an appropriate confidentiality agreement, it will also be granted the opportunity to conduct non-exclusive due diligence.
“The proposal is subject to due diligence and conditional on a number of other matters equivalent to the previously announced proposal.”