Greene's salary, which has stayed at the same level for five years, is tipped to jump to £535,000 from £498,000 after next month's General Election, said Sky News.
The decision is not yet finalised as consultations with key shareholders, including the Government, who still own 30 per cent of the privatised company, are yet to take place.
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Although insiders said it was "likely" that Ms Greene would be awarded the increase, which will be revealed in the postal service's annual report in June, directors were said to be determined to keep Greene.
Greene, a Canadian national, oversaw Royal Mail's controversial stock market flotation in 2013, which critics claimed left taxpayers short-changed after the company was significantly undervalued.
She was paid £1.35 million in salary and bonuses last year, according to the company's 2014 annual report.