Dutch government sources estimate the deal at 20 billion euros ($22 billion) or more, but German industry sources say it may be less.
TenneT had a book value of 7.3 billion euros at the end of 2022, on a balance sheet of 38.5 billion euros.
TenneT's German grid alone has liabilities of 21.6 billion euros, nearly three times that of the Dutch network.
TenneT's 19 billion euros of outstanding bonds, issued when interest rates were lower, are another issue, the people said.
Dutch pension fund PGGM, one of TenneT's bondholders, expects such an outcome in the event of a sale.