One of the sources said the purchase will likely happen via German state bank KfW, which will sell on the asset to private investors in a second step, while Berlin is expected to keep a blocking minority long-term.
The second source said a deal was close and could be announced in a matter of days.
Talks could still collapse, the sources said.
Bloomberg News first reported that a deal was close.
Sources told Reuters last year that a deal could value TenneT's German assets at 20 billion to 25 billion euros ($27.36 billion).
The Dutch government had no comment when contacted by Reuters and the German government did not respond to a request for comment.
The German government's plan to buy TenneT's business in Germany hit a hurdle after the country's constitutional court ruled that unused COVID-19 pandemic funds could not be re-used for climate projects.
