The CDSU is also expected to have talks next week with the Greens, The New York Times reported.
Merkel's conservative party and the center-left SDP took opposing positions on many issues while campaigning for the Sept. 22 election. Merkel, for example, promised not to raise taxes while the SDP proposed increasing taxes in the top brackets to raise money for infrastructure and education.
The CDU emerged with 190 seats, an increase over its previous performance, and its alliance with the Christian Social Union of Bavaria gives it 235 seats. But that is still short of a majority in the 630-member Bundestag, and its old partner, the Free Democrats, failed to win any seats.
Between 2005 and 2009, the Social Democrats joined a "grand coalition" during Merkel's first term as prime minister.
Celebrity Families of 2014 [PHOTOS]