In the aftermath of the diesel-cheating scandal, Mr Mueller sought to overhaul Volkswagen's rigid top-down management structure, delegating more responsibility to its brand and regional chiefs.
Diess' influence at Volkswagen would grow even further if the supervisory board supports long-standing plans to combine the carmakers' high number of independently operating brands into four core groups.
Sanford Bernstein analyst Max Warburton said Diess' track record of cost-cutting points to a more efficient VW under his leadership.
Mr Diess, a former BMW executive who joined VW in July 2015, has clashed with the company's labour leaders. That project became much more urgent as the diesel scandal generated massive costs, and meant taking on established interest groups.
Early in Diess's tenure as head of the VW vehicle brand, labour leader Bernd Osterloh publicly questioned his credibility in contract talks, raising concerns that he might fall victim to the carmaker's complex internal politics, which has toppled many high-profile newcomers. "Instead of being squeezed out, he has been pushed upward, and has been made CEO".
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. Audi, the VW brand, the trucks division, and the group's Chinese operations also have representatives on Volkswagen's top executive body.
Francisco Garcia Sanz, head of procurement since 2001, was picked by the board in 2015 to oversee the Dieselgate cleanup - he has now left the company too.
As head of purchasing at BMW, Diess was instrumental in the luxury-car maker's ability to weather the financial crisis by squeezing more than 4 billion euros out of supply costs. Now, he's poised to take VW's top job. That spurred his move to Volkswagen.
The change doesn't come as much of a surprise, because the VW Group issued a statement on Tuesday saying it was in the process of reviewing its senior management structure, which it explicitly said could result in personnel changes.