"If they come back it would have to be better than A$5.45, that's for sure," Gregg, who supported the original bid, told the Sydney Morning Herald.
The bidder, Airline Partners Australia (APA), said on Monday it was considering a new offer pitched at A$5.45 and other alternatives following the collapse of the world's largest airline takeover.
APA admitted defeat on Tuesday following three days of uncertainty after it failed to get 50% of shareholder acceptances for the bid by a Friday deadline.
Qantas said any new offer would be treated "as a completely new matter", which analysts said indicated it was unlikely to support a bid on the same terms. The Qantas board has faced heavy criticism over the failed bid from analysts, unions and some shareholders.
"APA's offer has lapsed, but we suspect its ardor has not. The same may not be said for the Qantas board," Goldman Sachs said in a note to clients.
Analysts said APA now had three options, to make a new offer at A$5.45 but with a lower level of minimum acceptances, come back with a higher offer or walk away.
Qantas has upgraded its earnings guidance three times in the past year but faces serious competition from the launch of a rival Australian domestic service from Asian airline Tiger Airways.
The bid group also included private equity firm Texas Pacific Group, Allco Finance Group, Allco Equity Partners and Canadian investment firm Onex.