Merkel's expressed skepticism about the latter two possibilities, and following an appeal from President Frank-Walter Steinmeier, Schulz agreed to meet with the chancellor and CSU leader Horst Seehofer on Thursday night to talk about the various possibilities.
"What I can tell you is that we discussed the situation at the SPD party board meeting intensively".
Merkel is casting around for a coalition partner after her centre-right bloc shed support to the far right in the 24 September election.
"We should discuss each of these options", he said, and ruled out any hasty decisions under time pressure.
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".
Ahead of that congress, which will also decide whether to re-elect Schulz as chief of the SPD, the party's top brass has been careful to tread softly regarding its options.
GettyMrs Merkel has been accused of trying to lead the whole of Europe from Germany
Meantime, she continues to head a caretaker government made up of her conservatives and the Social Democrats.
"It's now up to the SPD to provide clarity", said CDU manager Klaus Schueler.
"We need a different Europe and the initiatives that the French president has suggested should not be given a "no" from Berlin or left unanswered", he said, referring to Macron's ideas of creating a new eurozone finance minister position and giving the 19-member zone its own budget.
"It's not automatic that there will be a new grand coalition", Schulz told reporters in Berlin.
Schulz, a former president of the European Parliament, has said he wants changes in Germany's approach to the European Union and in economic and social policy.
"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.