(Adds detail on bid, background)
Oct 8 (Reuters) - Australian Unity Office Fund AOF.AX said on Monday that funds managed by Starwood Capital Asia Ltd raised their buyout offer for the real estate investment trust for a third time, making the deal potentially worth A$480.4 million ($338.9 million).
Australian Unity Office said the funds sweetened their bid to A$2.95 per cash unit, 8.5 percent higher than the last offer of A$2.72 cash per unit.
The offer represents a premium of 9.7 percent to the trust's last close.
Australian Unity Office Fund's independent board committee said it was in the interests of unitholders to engage further with Starwood.
The Melbourne-based company plans to grant Starwood, a private equity firm, up to four weeks to complete its due diligence and finalise the proposal, it said in a statement.
Australia's commercial property sector is defying a softening in home values, with city downtown capacity barely growing and demand outstripping supply.
The rising demand has spurred a bidding war between Canadian landlord Oxford Properties Group and private equity giant Blackstone (NYSE:BX) Group BX.N for Australian office owner Investa Office Fund IOF.AX . = 1.4174 Australian dollars)