UPDATE: VW denies the report.
"Diess would go in right away if he could," the magazine quoted one of Diess' top managers as saying.
Diess believes Volkswagen could profit from Tesla's competence in the fields of batteries and software, Manager Magazin said, adding the German company had enough money.
Acquiring a stake would be sufficient for a start, the report said.
A bigger obstacle, however, would be to get the consent of Volkswagen's dominating owner families, the Piechs and the Porsches.
Volkswagen was not immediately available for comment.
A banker close to Volkswagen said that while it is true that Diess would love to have Tesla's software developers, he believed it is almost impossible to justify paying $30 billion (27.09 billion euros) to buy the whole company.
Reporting by Thomas Seythal; Additional reporting by Jan Schwartz and Edward Taylor.