Mr. Matthias Müller showed his general willingness to contribute to the changes.
The company said it was contemplating a management reshuffle and reassigning responsibilities among executives that "could include a change in the position of the chairman of the board of management", the German term for CEO.
Both Bloomberg and "Handelsblatt" are reporting that current VW brand chief Herbert Diess is to replace Mueller.
"The Volkswagen brand's first-quarter delivery results are very encouraging".
It is unclear how soon Diess, a former BMW BMWG.DE executive who joined VW in July 2015 and has clashed with the company's labour leaders, might replace Mueller.
The supervisory board will vote on the change in top leadership at a meeting on Friday, according to people familiar with the matter, who asked not to be identified speaking ahead of an official announcement.More news: English Premier League match report Arsenal v Southampton 08 April 2018
Despite facing billions in fines, vehicle refits and lawsuits relating to its "dieselgate" scandal, Volkswagen's operating results have been robust under Mueller's watch, with sales and profit hitting record highs previous year.
"If Diess is confirmed as the successor, VW shares will extend their gains", Evercore ISI analyst Arndt Ellinghorst said, who has an "outperform" rating on the stock.
The company said in its statement on Tuesday that it was considering changes to its complicated management structure. No further information was made available with regards to the precise fate of acting CEO Matthias Mueller.
While Mueller is a lifelong VW veteran, at times he cut an uneasy figure as CEO, which required him to manage the often contradictory demands of angry auto owners, disgruntled investors, well organized workers, and state officials with their own political agendas.
Its complex structure has extended to its main shareholder, Porsche Automobil Holding, where VW's chairman serves as the CEO and Mueller also serves as a top executive.
Citing company sources, the German newspaper Handelsblatt reported that Mueller is about to be replaced by Herbert Diess, an executive who now leads the Volkswagen brand. The works council, whose members occupy half the seats on the supervisory board, also declined comment.