"What I can tell you is that we discussed the situation at the SPD party board meeting intensively".
Other options apart from a grand coalition include a minority conservative government - which the SPD could support on a case-by-case basis, or fresh elections.
Schultz had initially refused to consider another "grand coalition" with Merkel after a disastrous showing of the Social Democrats in the election on September 24, saying the Social Democrats needed to go into opposition.
In a sign of the ongoing friction between Schulz and Merkel's bloc that may make negotiations hard, he blamed the Bild report on a leak from her side and said he had telephoned her Friday to say it was "unacceptable". By contrast, Steinmeier - himself a former SPD leader - is known to favor the grand coalition option.
Merkel is facing the most serious political crisis since she assumed office 12 years ago after the breakdown of the government coalition exploratory talks on November 19.
"Whoever circulates false reports destroys trust", he said.
Speaking after Schulz's statement, CDU chief executive Klaus Schüler said his party respected what the SPD chairman had to say and would wait for the Social Democrats to make a decision about whether to officially pursue talks.
Merkel told the party conference that she wants to "come quickly to a government", adding that Germany must have a stable government, "but also a government that really advances the country".
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The unusually testy tone Schulz struck is a reflection of the differences between conservatives and Social Democrats not just over the policies of a possible grand coalition, but whether even to try to form one at all.
Meantime, she continues to head a caretaker government made up of her conservatives and the Social Democrats.
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Firmly denying that an agreement had been reached on opening negotiations on a grand right-left coalition, Schulz said that all options remained on the table.
However, Schulz softened the stance on Friday as he said his party was willing to hold talks with the Union.
In particular, he said he would demand German support for Emmanuel Macron's proposals for a Brussels-based finance minister and single budget for the Eurozone.
"Giving Emmanuel Macron a positive answer will be a key element in every negotiation with the SPD", Schulz was quoted as saying in the interview made available on Friday, adding that he also backed a joint European Union tax policy.