If confirmed, Osterloh's exit could weaken resistance to faster and more drastic restructuring at the German carmaker.
Last year, the 64-year-old opposed an attempt by Diess to extend his contract as the CEO strives to cut costs and free up resources to invest more in electric vehicles.
Osterloh has been a member since 2005 of the supervisory board at Volkswagen, where under Germany's system of corporate governance labour representatives make up half the board.
He has instead been offered the position of personnel director at Traton, Volkswagen's truck unit that was spun off and separately listed in 2019, one source said.
A second source said the group was considering proposing a new labour representative to its board, but did not give a name.
Volkswagen, its main shareholder Porsche SE and the works council declined to comment.
Five sources told Reuters that Volkswagen would in the near future debate an important change in the composition of its supervisory board, adding no final decisions had been taken.
One said announcements on labour representation at Volkswagen were expected on Friday. Another said Traton's supervisory board would meet on Friday.
The move would follow a surge in Volkswagen's shares, as investors warm to its efforts to overtake Tesla and become a world leader in electric cars.
The stock has risen by more than half in value so far this year, giving Volkswagen a market value of 132 billion euros ($159 billion).
Should Osterloh leave the supervisory board, as would be required should he take up an executive role at Traton, the most likely candidate to replace him would be deputy works council head Daniela Cavallo, the sources said.
Any nomination would be subject to a confirmatory vote by shareholders at the annual meeting in July.
($1 = 0.8291 euros)
(Writing by Douglas Busvine. Editing by Keith Weir, Mark Potter and Alexander Smith)
By Christoph Steitz and Jan Schwartz
