Early on Wednesday Qantas Airways rejected an offer valuing the company at US$8.6 billion, which is 25 per cent above its share price.
That deal would have been the largest ever Australian buyout, but analysts have suggested the deal fell down because of a number of "complex conditions" which were attached to it.
However, the Financial Times has reported that Qantas is expected to accept a new $8.75 billion offer from the consortium on Thursday.
One source close to the negotiations told the FT: "There will be more talks late into the night but we are 99.9 per cent there. The sides have come to an agreement, the rest is just formalities."
Macquarie Bank has said it will own a share which is less than 15 per cent, while Allco Finance Group is set to own an 11 per cent stake in Qantas.