The company has denied the report.
"Diess would go in right away if he could," the magazine quoted one of Diess' top managers as saying.
The automaker issued a statement calling the report "without merit."
"The speculation about buying a stake in Tesla made by Manager Magazin is without merit," a Volkswagen spokesman said in a written statement to Reuters.
The magazine reported that Diess believes VW could profit from Tesla's competence in the fields of batteries and software. A big obstacle would be to get the consent of Volkswagen's dominating owner families, the Piechs and the Porsches.
A banker close to Volkswagen said Diess would love to have Tesla's software developers but it is almost impossible to justify paying $30 billion to buy the whole company, the report said.