The cash and scrip offer from Qube, along with partners Global Infrastructure Partners and Canada Pension Plan Investment Board, implied a value of A$9.25 per Asciano share, a 5.9 percent premium to Monday's close, and valuing the target at A$9.02 billion ($6.35 billion).
Asciano said its board was considering the proposal. It also said it would continue to unanimously recommend Brookfield's A$9.22 a share cash-and-scrip bid formally announced on Monday "in the absence of any superior proposal capable of acceptance."
Qube already owns one-fifth of Asciano shares after late night raid last month and has vowed to oppose the Brookfield takeover. Brookfield responded by buying its own near 20 percent stake last week.