Volkswagen declined to comment.
Handelsblatt had reported the news earlier.
At Seat, Diess would be succeeded by current technology head Thomas Schmall and at Skoda by Murat Aksel, head of procurement on the Volkswagen board, the source added.
Volkswagen has been heavily focused on regaining lost ground in the fast-growing field of software-heavy electric cars, where United States and Chinese manufacturers are seen as having a lead.
(Reporting by Jan Schwartz, Thomas Escritt and Christoph Steitz; Editing by Madeline Chambers and Hans Seidenstuecker)