No further information was made available with regards to the precise fate of acting CEO Matthias Mueller.
The Associated Press reports the automaker said it was looking at a reshuffle of management and responsibilities, and German news media is reporting Muller's position could go to VW brand head Herbert Diess.
"It is now open whether the considerations and discussions will lead to a further development of the management structure or to personnel changes", VW said in the statement. The shares jumped on the news and were up 4 percent at 170.72 euros at 1325 GMT.
Supervisory board chief Hans Dieter Poetsch had been "speaking with different members of the supervisory and executive boards" about moving or replacing some of them, it went on, adding that Mueller "signalled he was open to play a part in the changes".
Mueller took more than unexpectedly in 2015 when predecessor Martin Winterkorn fell prey into the corporation's scandal in excess of cars rigged to cheat on diesel emissions tests.
Two people close to the carmaker said its supervisory board was due to meet on Friday, and would also discuss a possible stock market listing for the company's truck and bus division - another move aimed at creating a more focused business.
The management revamp comes after the company posted record profit past year.
Investors sent stock in scandal-hit auto giant Volkswagen surging Tuesday, as the firm announced it was considering reshuffling its board and replacing chief executive Matthias Mueller.
However, Volkswagen refused City AM's request to confirm whether Muller was resigning, and whether he would be replaced by Diess. But when Winterkorn fell, he had only been with the company for less than three months. Prior to joining the Wolfsburg-based automaker in 2015, Diess was BMW's head of development, and is widely credited with slashing costs.