Discovery in 2015 won the European broadcast rights for the Olympics from 2018 to 2024 for 1.3 billion euros (1.14 billion pounds), beating national public broadcasters such as the BBC and France Television.
It had been expected to pass on some lucrative rights. But last November ARD and ZDF said they would not show the Olympic Games for the first time, having failed to clinch a deal.
According to FAZ, the renewed negotiations are focused on the 2018 Winter Olympics in Pyeongchang for the moment, but the paper said a cooperation on subsequent Games had become more likely.
Discovery, ARD and ZDF were not immediately available for comment on the report.
The paper quoted Susanne Aigner-Drews, the head of Discovery's German business, as saying: "Discovery has always emphasised that it is our desire to cooperate with partners that value the Olympic Games."
ZDF told FAZ only that it was in contact with Discovery, pointing to the fact that the German broadcaster holds the broadcast rights for the Paralympics.
German monthly Manager Magazin said last year that initial talks between Discovery and ARD and ZDF had stalled over the price of a sub-licence.
The magazine said at the time that ARD and ZDF wanted to pay no more than 100 million euros for the broadcast rights in Germany, while Discovery was demanding at least 150 million.
(Reporting by Maria Sheahan; Editing by Mark Potter)
