Europe's largest automotive group has been considering measures to make itself more nimble, including carving out truck operations via a stock sale, as it spends billions of euros on electric cars and new mobility services.
Diess, 59, has been pushing restructuring at the VW brand and repeatedly clashed with powerful labor unions over cost reductions.
Mueller's likely departure comes two days after Deutsche Bank dismissed CEO John Cryan in search for profit and change, replacing him with retail banking chief Christian Sewing.
VW shares rose on the news in markets around the world.
"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. "We see no better alternative to Matthias Mueller to make the company fit for the future."
The management upheaval contrasts with a strong operating performance at the carmaker which last year posted record auto sales and profit.
Tug of war
But the persistent tug of war between VW's controlling families, unions and stakeholders have made it difficult to effect structural change that investors have said is key to VW fulfilling its potential.
Mueller had expressed his general willingness to participate in the changes, VW said on Tuesday, but added that it was still to be determined whether efforts to develop a new leadership structure would leave him in place.
Chairman Hans Dieter Poetsch is currently in talks about changing the structure with fellow supervisory board members and members of the management board, VW said.
Two months ago, sources close to the top management of VW told Reuters that Mueller was growing frustrated with a lack of support for his reform efforts and by the company’s inability to draw a line under its emissions scandal.
Volkswagen declined to comment on whether the board was poised to name Diess as new CEO. The works council, whose members occupy half the seats on the supervisory board, also declined comment.