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.
The takeover battle underscores the attraction of Australian companies in a year in which the local currency has skidded 13 percent and shares have fallen 4 percent, cutting valuations of firms seen as well regulated and having growth potential.
Asciano, which has rail in every Australian state and stevedoring in 40 locations, has been seen as especially vulnerable because its earnings have been hit by a resources slowdown, while it is expected to benefit from restructuring aimed at automating ports and cutting costs.
Under Qube's offer, Asciano shareholders will receive a combination of cash and Qube shares, helping them retain an exposure to Asciano's container terminal businesses and participate in the growth opportunities of Qube.
The Australian Competition and Consumer Commission (ACCC) has also suggested it might stop Brookfield buying Asciano since the Canadian suitor already owns some of the railways Asciano's trains run on. It is due to make a final ruling on Dec. 17.