Winterkorn said in a video statement on Tuesday that he was "terribly sorry to have broken the trust" of millions of people around the world.
"The irregularities of these engines contradicts all that Volkswagen stands for," he said, promising to work "quickly, thoroughly and transparently" to answer the public's questions. "Manipulation and Volkswagen, that must never happen again."
"We will do everything we can to earn your trust back, step by step," he added.
Regional daily Tagesspiegel previously reported on Tuesday that Winterkorn could be relieved of his duties by the automaker's supervisory board in the wake of the pollution cheating scandal.
Winterkorn, 68, who earlier this year successfully averted a campaign by then supervisory board chief Ferdinand Piech to remove him, no longer enjoyed the board's confidence, the newspaper said, quoting "supervisory board sources."
The board's six-member steering committee would meet on Wednesday and Winterkorn's fate could be officially decided by the full 20-strong board on Friday, the paper reported.
Winterkorn, who has served as CEO since 2007, would reportedly be replaced by Matthias Müller, head of VW's luxury sports car arm Porsche, it added.
Volkswagen was not immediately available to comment on the report.
The group, previously regarded as a paragon of German industry, revealed Tuesday that 11 million diesel cars worldwide are equipped with devices that can cheat pollution tests in a rapidly snowballing scandal that has wiped a third off VW's market capitalisation in just two days.
Winterkorn is a former protege of Ferdinand Piech, 78, a grandson of VW's founder who served as CEO between 1993 and 2002 and then became its supervisory board chief.
In an ugly leadership battle between the two men earlier this year, Piech tried to oust Winterkorn because of the latter's difficulties in making substantial inroads into the US market, as well as VW's over-dependence on the Chinese market.
But other supervisory board members rallied behind Winterkorn, finally forcing Piech himself to resign in April.
Earlier this month, before the scandal broke, the six-member steering committee had "voted unanimously" to propose to the 20-strong supervisory board that Winterkorn's contract be extended until December 31, 2018.