The meeting, at which the sources said the board could decide in favour of a two-year extension for Diess until 2025, is taking place only days ahead of Volkswagen's strategy day scheduled for July 13.
A fresh contract would come shortly after Diess' long-term opponent Bernd Osterloh stepped down as works council head and took a management position at Volkswagen's truck unit Traton.
Diess, whose current contract runs until April 2023, had asked for an early extension towards the end of last year to get more backing for his efforts to reform Europe's top carmaker, but ran into opposition from powerful labour leaders, including Osterloh.
No firm decision has been taken and there is no guarantee that the supervisory board will reach an agreement at its meeting on Friday, the people said, adding several details still had to be hammered out.
A spokesperson for Volkswagen's supervisory board declined to comment.
An extension would give Diess the mandate to fulfil Volkswagen's declared ambition to become the world's largest electric vehicle maker by the middle of the decade and overtake key rival Tesla.
Diess, a former BMW executive, joined Volkswagen's management board in July 2015 before becoming CEO in April 2018 and has been the key driver behind the group's effort to transform itself.
(Additional reporting by Ilona Wissenbach and Christoph Steitz; Editing by Kirsten Donovan)
By Jan Schwartz