The Australian Financial Review reported that the shares were being offered at A$1.05 and the deal was worth A$400 million ($378 million). A spokeswoman for UBS was unavailable for comment.
Warburg Pincus became a cornerstone investor in Brisbane-based Transpacific in 2009 when it bought a 33.9% stake at A$1.80 a share. It is the first and only investment in Australia for the global private equity group.
Earlier this week, Transpacific said it had hired Deutsche Bank to sell its New Zealand waste management unitwhich has previously been reported as being worth NZ$900 millionto focus on growing its Australian arm.
Shares in the recycling, waste management and industrial services firm rose to their highest level in more than two years this week and closed at A$1.12 on Friday.