The 64-year-old Mueller, who took over in 2015 and has worked inside the Volkswagen structure his entire adult life, has two years left on his current contract.
Shares in Volkswagen jumped on the news, and closed up 4.5 percent at 171.58 euros. A timeline as to how soon Diess could replace Mueller is unknown.
The statement said board of directors head Hans Dieter Poetsch was in discussions with top managers about how their responsibilities are divided. VW officials had no statement beyond the two-paragraph filing.
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.
As the executive overseeing VW's biggest unit, he routinely butted heads with the powerful labor union as he sought to cut costs and simplify the structure of the carmaker during the crisis.
It shouldn't be a surprise to anyone that the last few years at Volkswagen haven't exactly been smooth sailing.
"The potential change in CEO comes as a surprise", Christian Ludwig, a Bankhaus Lampe analyst, told Bloomberg News.
Under Mueller - who was promoted to the top job in the chaotic days following the public disclosure of the diesel cheating - VW has weathered the blows from the scandal while embarking on an aggressive expansion into electric cars. He has led the company through the scandal to record sales and strong profits.
The auto maker also managed to fend off Toyota Motor to retain its status as the world's largest vehicle maker.
BMWDiess, who has been pushing for changes in the brand's structuring, joined the company in mid-2015 before the diesel scandal broke.
Two people close to the carmaker said that VW's supervisory board was due to meet on Friday and would also discuss efforts to pave the way for the IPO of VW's truck and bus division.
These changes could, according to the company, be personnel changes and changes in the specific responsibilities of management members.
A representative of the German state of Lower Saxony, another of the largest shareholders, was not immediately available for comment on the appointment.