Without citing its sources, Spiegel said Karlheinz Blessing, who was appointed management board member with responsibility for human resources on January 1, 2016, would be replaced by Gunnar Kilian, secretary general of VW's works council.
The statement added: "It is now open whether the considerations and discussions will lead to a further development of the management structure or to personnel changes". This could include "personnel changes in the board of management" and different responsibilities for its members, the Wolfsburg-based business said.
German newspaper Handelsblatt first reported that Diess would replace Mueller.
In tapping the 59-year-old Diess for the top job, Volkswagen would elevate a senior executive from its own ranks, while handing the reins to someone who was not at the automaker when the diesel cheating began.
Mr Diess, 59, has been prepared for the role after being headhunted from BMW in 2015 less than three months before the revelation that VW had fitted 11 million diesel cars worldwide with "defeat device" software created to cheat official emissions tests.
Diess is due to outline the group's new leadership structure in front of the supervisory board on Friday, two sources said.
Mueller's likely departure comes two days after Deutsche Bank DBKGn.DE , another pillar of corporate Germany, dismissed its chief executive, John Cryan, in pursuit of a more rapid turnaround following years of losses.
"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. Since admitting to the scandal, VW has paid out nearly €25 billion in fines, compensation, recalls and refits.
Volkswagen is expected to make a final decision regarding the future of its top executive in Matthias Muller by the end of the week amidst the company's costly diesel emissions scandal.
The company said in its statement on Tuesday that it was considering changes to its complicated management structure.
Volkswagen will give labor leaders a management board seat as part of a broad agreement to win approval for Herbert Diess as the German carmaker's new chief executive, sources said on Wednesday.
A Volkswagen spokesman declined to comment on the rumours when contacted by AFP.