Mr Schulz is facing open revolt in his Social Democratic Party (SPD) which is considering throwing a lifeline to Mrs Merkel but is driving a hard bargain for the party’s support.
The former European Parliament President is under pressure to reverse his decision to take the SPD into opposition following its worst ever result in September’s election.
He is already facing tough talks with President Frank-Walter Steinmeier in a bid to break the deadlock. Mr Steinmeier, himself a former SPD leader, is said to be furious at the party’s stance.
And it has become clear Mr Schulz is also facing a rebellion from within his party over his refusal to consider talks.
More than 30 MPs have spoken out against Mr Schulz’s position and demanded he took a more flexible approach.
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Mr Schulz said struck a more conciliatory tone when he emerged from an internal party meeting.
He said: “The SPD is fully aware of its responsibility in the current difficult situation.
“I am sure that we will find a good solution for our country in the coming days and weeks.”
Germany faces a fresh general election if Mrs Merkel is unable to form a new coalition government and SDP bosses fear even greater losses in a new ballot.
Questions of Mr Schulz’s leadership are now being raised after a number of senior MPs from the party broke ranks to criticise his stance.
He faces an annual vote to confirm him as party leader next month and his position is not guaranteed.
SPD MP Johannes Fechner said: “The SPD should not rush to call for new elections but should take the conversation with the president seriously.”
Party colleague Bernd Westphal said: “We have to consider the conditions under which we would agree to go into coalition.”
Mr Schulz led the SPD to its worst ever result in September, and current polls suggest the party could do even worse in new elections.
Sources in the party say they have been fielding phone calls from supporters asking if they are “crazy”.
Germany has not had a minority government since the Second World War, and there are deep misgivings over the idea — not least because it was a series of minority governments in the 1930s that led to the rise of the Nazis.
Mrs Merkel said she would prefer new elections but under the German constitution, only President Steinmeier has the power to call new elections or appoint a minority government.
Analysts warn a minority government would be bad for Britain, with Mrs Merkel forced to seek approval from parliament over every stage of Brexit negotiations.