The companies had until today to submit their final offers for the business.
A report by Reuters said the final bids were backed by bank financing with Blackstone sourcing their financing from US markets and TPG using a consortium of commercial banks.
Blackstone was thought to have ducked out of the process in December amid company founder Bob Ingham asking for about $1.4bn for the business, but had had its interest reignited with the entry of TPG.
At the time it was thought that offers for the business would value it at less than A$1bn after Ingham reduced his asking price. The previous figure was based on the business fetching seven-times its fiscal 2013 earnings.
The report added that Ingham could consider an IPO if the trade sale does not come off.
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