The 64-year-old Mueller, always a reluctant CEO who had grown tired of the regular grillings by board members, responded during the talks by signaling he was prepared to step aside, they said.
Volkswagen is now embroiled in infighting between with the most prominent stakeholders - including the Porsche and Piech families - and the German state of Lower Saxony and labour leaders, but the news of a potential new head for the company saw share prices rise by 4.5 percent yesterday to just under £150 a share.
Under Mueller - who was promoted to the top job in the chaotic days following the public disclosure of cheating in emissions tests - VW has weathered the blows from the scandal while at the same time embarking on an aggressive expansion into electric cars. The scandal has cost the company over $30 billion. Amid opposition from labor leaders, Mueller failed to sell motorbike maker Ducati a year ago. Its profit margin climbed to 7.4 percent of sales previous year from 6 percent in 2015, when the crisis hit.
The issue with restructuring VW lies with a tug a war between interested parties including the controlling families, stakeholders, and unions. But when Winterkorn fell, he had only been with the company for less than three months.
Volkswagen said on Tuesday Mueller had expressed his general willingness to participate in a management overhaul, and it was still to be determined whether efforts to develop a new leadership structure would leave him in place.
"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.
Prior to joining VW, Diess was an executive at BMW.
VW shares got an additional boost from the reports that it is planning on replacing Mueller. Previous executives including Bernd Pischetsrieder and Wolfgang Bernhard struggled to push through such reforms. According to the company, final decision is expected to be made by the end of the week. Mueller told German magazine Der Spiegel in March that he "doesn't like politicians meddling with my business", likening a discussion about a salary cap for executives to the oppressive system of the former German Democratic Republic. Other potential CEO candidates include Volkswagen's trucks chief and Daimler veteran Andreas Renschler.