The clock is ticking for ExxonMobil(XOM) - Get Report as it rushes to finalize an indicative offer for Papua New Guinea-focused gas explorer InterOil (IOC)  but it is Total(TOT) - Get Report that will be feeling the pressure.

Exxon has until July 28 to finalize its offer ahead of an InterOil shareholder vote on a $2.2 billion cash-and-share bid from Oil Search, the junior partner in the onshore PRL15 license, gas from which will underpin the Total-operated Papua LNG Project.

Exxon has not identified itself as the mystery bidder announced by InterOil last week, but reports in Australian newspapers named the Irving, Texas giant as the interloper. These were corroborated by two sources involved in the InterOil bidding. JPMorgan Chase is acting as Exxon's adviser, according to The Australian, though that could not be confirmed.

InterOil, Exxon and Total all declined to comment, while JPMorgan spokespeople were not immediately available.

It would certainly be a surprise if Exxon wasn't involved as it undoubtedly has the most to gain from a bid. InterOil's 36.5% stake in PRL15 license, which contains the prize Elk-Antelope field, is located close to the Exxon-operated PNG LNG, not to be confused with Papua LNG. Gas from Elk-Antelope will be piped along the same offshore pipeline route as PNG LNG and ultimately shipped from the same port, just to the North of Papua New Guinea's capital Port Moresby.

Oil Search, which has stakes in both Papua LNG and PNG LNG, said in May its bid for InterOil aimed to promote a combination of the two projects. UBS analysts in April forecast that Papua LNG would likely cost $15 billion to build (though Total claims a figure closer to $10 billion), while a planned extension of PNG LNG will cost about $9 billion. Combining those two projects would save about 10% of the total cost, or between$1.9 billion and $2.4 billion, UBS suggests. Oil Search also claims to have identified operational savings, though it has declined to put a figure on them.

Exxon owns 33.2% of PNG LNG but none of the Papua LNG project. Buying InterOil would secure it a 36.5% stake in Papua LNG, boosting its potential savings from a merger.

Oil Search owns 29% of the PNG LNG project and will own 29% of Papua LNG, up from 22.8%, if its offer for InterOil finalizes. Missing out on a further 6.2% of the Papua LNG would hurt but hardly be catastrophic given its already minority and non-operating position in both projects.

Total, which is effectively financing Oil Search's bid with $1.67 billion of secondary agreements to buy most of InterOil's assets, has more to lose. The French company will emerge with 48.1% of the Papua LNG project if Oil Search's bid is successful, up from its current 40.1%. Just as importantly Total will have a far stronger hand in negotiating the inevitable merger of Papua LNG and PNG LNG with Exxon.

Total chairman and CEO Patrick Pouyanné underlined the importance of increasing Total's stake in Papua LNG when he noted that it would enable Total to "drive the (project's) future development."

Total will not happily see that control diluted, least of all at the expense of massively strengthening Exxon's hand.

InterOil investors appear to be counting on it. The target's shares last closed July 1, at $46.74, a 12% premium to Oil Search's offer of $55.54 ($41.67), or 8.05 shares. Oil Search shares closed Tuesday at A$6.90