However, if this will push through, such a deal will surely be one of the most remarkable in this era since the combined market value of the firms could go over $350 billion, with Exxon making up the $190 while Chevron's is $164 billion.
"The turnaround story will take some time", said Biraj Borkhataria, analyst with RBC Capital Markets, noting that the company is not yet covering its dividend and capital spending with cash from operations.
Still, the benefits of a deal in the current environment are clear.
But an Exxon-Chevron tie-up would likely face significant hurdles under President Biden, who wants to combat climate change by making the United States less dependent on oil and investing in renewable energy.
Exxon previous year slashed spending on new projects by almost a third, outlined plans to cut up to 15% of its workforce while adding $21 billion to its debt to cover its spending and restructuring.
Exxon posted a net loss of $20.2 billion, or $4.70 per share, in the fourth-quarter ended December 31, compared with a profit of $5.69 billion, or $1.33 per share, a year ago.
In afternoon US trading, Exxon shares rose almost 2% while BP shares dropped more than 6%.
Last year's Saudi-Russian oil price war, for instance, highlighted the vulnerability of US producers to foreign governments that can effectively dictate the price of crude by forcing energy companies they back to boost or cut output. Last week the company reported a fourth quarter loss.
USA oil companies each compete among one another and set their own varying production targets, with limited ability of Washington to intervene.
Yet they also felt the pain.
OPEC back in October said that the COVID-19 pandemic had created the sharpest fall in energy and oil demand "in living memory". Equally, this could be the beginning of one of the biggest corporate mergers ever. Prices have since rebounded to roughly $52 a barrel.
Exxon and Chevron declined to comment on the Dow Jones report. Exxon late last year left its dividend flat after boosting the shareholder payout each year since 1982.