ExxonMobil, as operator of PNG LNG and Oil Search's partner across a swathe of exploration and production licences in Papua New Guinea, is the most logical rival bidder for InterOil, which has discovered the Elk-Antelope gas-condensate fields.
Bringing Elk-Antelope gas into an expanded PNG LNG, or at least finding greater synergies with the proposed Papua LNG project, is something Oil Search has been open about, while ExxonMobil is keen to fast-track an extension of the successful PNG-LNG.
InterOil has a large, disaffected shareholder base, as proven at last month's special meeting called by founder and dissident shareholder Phil Mulacek, and shares in the takeover target surged almost 4% on Friday as investors reacted positively to the prospect of a bidding war emerging for the company after the earlier decision by directors to back the $US2.2 billion bid by Oil Search.
Oil Search is offering 8.05 of its shares for each share held in InterOil, along with a listed contingent value right, which will give InterOil shareholders access to any increase above 6.2 trillion cubic feet equivalent of oil and gas in the Elk-Antelope field.
InterOil said last week it had received as an "unsolicited, conditional, non-binding proposal", and while the board was considering it the Oil Search bid remained the preferred option.
ExxonMobil isn't talking about whether it is the bidder, and the structure of its offer remains unknown.
Oil Search is offering to allow InterOil shareholders continued exposure to Elk-Antelope, and with the backing of Total it is offering an attractive top-up cash payment based on the next reserves report, due in to 2017, to help capture the upside from ongoing appraisal drilling.
Shareholders are expected to consider the Oil Search offer on July 28, and based on last month's numbers a positive result for Oil Search seems even less likely - although the quantum offered by the mysterious third party, either ExxonMobil or someone else, would been to be substantially higher to sway shareholders.
Beyond ExxonMobil there are no obvious bidders, and with the need to get the PNG government support, a rank outsider seems unlikely.
InterOil's shares finished trading on Friday at $US46.74, their highest level since mid-2015, valuing the entire company at $US2.32 billion, which is ahead of the Oil Search offer.
Mulacek argues Elk-Antelope contains as much as 15Tcfe.