Schulz has repeatedly said the SPD would not return as the junior coalition partner in a government led by Merkel, after suffering a stinging defeat in September's general election.
But after Merkel's bid at forging a coalition with other parties fell apart, plunging Germany into a political crisis, voices within and outside the SPD have grown louder in questioning Schulz's decision and push for another election.
President Frank-Walter Steinmeier, who holds the power to call snap polls and who is himself a senior Social Democrat, has said that this "is the moment when all participants need to reconsider their attitude".
The president has already held talks with the leaders of parties in the failed coalition talks -- the pro-business FDP -- which halted the negotiations, the ecologist Greens and Merkel's Bavarian allies the CSU.
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As the crisis shows no signs of abating, the Sueddeutsche daily reported that "in the SPD, unease is growing over its clear refusal of a grand coalition".
"One must speak with the president openly, without already insisting on your own point of view," Johannes Kahrs, who leads the right-leaning wing of the SPD, told Bild daily.
EU Budget Commissioner Guenther Oettinger also urged the SPD to reexamine its stance.
Schulz himself told national news agency DPA today that he is "certain, that we will find a good solution for our country in the coming days and weeks".
He added that his party "is well aware of its responsibility in the current difficult situation."
Schulz's comments came as Bild reported that "resistance is growing" against him.
The "most prominent secret advocate for a new grand coalition is deputy chancellor Sigmar Gabriel", added Germany's top-selling daily.