The business could be valued as around NZ$880m ($720m), said Reuters, citing people familiar with the matter.
Australian private equity firm Archer Capital has also advanced in the auction, said the sources.
The three firms are currently working with banks on debt packages for the bids, according to the people.
Last month Warburg Pincus exited its investment in Transpacific Industries for AUD$570m ($541m).
Warburg Pincus acquired the stake back in 2009 via a placement and rights issue. The firm has invested around $522m in the company, according to a Reuters report.
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