"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.
Shares in Volkswagen jumped on the news, and closed up 4.5 percent at 171.58 euros.
In tapping the 59-year-old Diess for the top job, Volkswagen would elevate a senior executive from its own ranks, while at the same time handing the reins to someone who was not at the automaker when the diesel cheating took place.
Volkswagen had stated earlier this week that it was looking at a change in leadership as part of a broader management overhaul but had not given details.
BMWDiess, who has been pushing for changes in the brand's structuring, joined the company in mid-2015 before the diesel scandal broke.
Longtime CEO Winterkorn quit after the firm admitted in 2015 to manipulating 11 million diesel vehicles worldwide to cheat regulatory emissions tests in a scandal that became known as "dieselgate".
According to VW's statement, Mueller showed "general willingness to contribute to the changes".
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Volkswagen (VOWG_p.DE) will give workers a management board seat to try to secure agreement for a far-reaching reform of the company under a new chief executive, sources familiar with the matter said on Wednesday.
The issue with restructuring VW lies with a tug a war between interested parties including the controlling families, stakeholders, and unions.
As part of the streamlining plan, Volkswagen tried to sell motorbike manufacturer Ducati past year, but failed in the face of opposition from labour union leaders.
Diess and Mueller instead agreed to guarantee VW's German jobs until 2025 to get labour approval for a plan to turn the carmaker into a mass producer of electric cars.
German newspaper Handelsblatt first reported that Diess would replace Mueller. Other potential CEO candidates include Volkswagen's trucks chief and Daimler veteran Andreas Renschler. Despite the product reform, Mueller has so far struggle to make Volkswagen a more efficient and focussed company which was planned.
VW could move as soon as Friday to name Herbert Diess, head of its Volkswagen brand, as its new leader. The company declined to comment further.