As of 0830 GMT, France's 10-year debt hit 0.772 percent on the secondary market, while the German 10-year Bund fell to 0.484 percent.
"Factors causing the recent risk-off mode are unlikely to fade rapidly," BNP Paribas analysts said in a note.
"Greece and the question of QE (stimulus) are keeping bond markets nervous," it said, adding that the anxiety is likely to persist through January.
At the weekend, Spiegel quoted German government sources as saying that Berlin sees a Greek exit from the eurozone as "almost inevitable" should Greece's radical leftist Syriza party win snap elections on January 25.
Both Chancellor Angela Merkel and her finance minister Wolfgang Schaeuble have come to consider that Greece's departure from the single-currency bloc would be "manageable", the magazine said.
German media saw the Spiegel article as an attempt by Merkel and Schaeuble to put pressure on Greeks and Syriza leader Alexis Tsipras, who has vowed to end austerity policies.
The spectre of a Greek exit from the eurozone caused major stock markets to fall on Monday despite a European Commission declaration that eurozone membership was irrevocable.