1 NEW ROUND OF NEGOTIATIONS
Chancellor Angela Merkel could suggest a cooling-off period for the four parties which have been locked in talks for more than a month, before coming together again for a new round of negotiations.
But fundamental differences between the parties over immigration, environmental protection and Europe are unlikely to go away.
Dragging out the negotiation process also risks seeing parties harden their positions.
But as Germany's Constitution does not prescribe a deadline to form a government after an election, Dr Merkel could sit tight as leader of a caretaker government until the parties find a compromise.
2 ANOTHER COALITION PARTNER
Dr Merkel can in theory turn to the Social Democratic Party (SPD), which has been her junior coalition partner for the past four years. Mathematically, it would also be the most stable option as together, Dr Merkel's conservative alliance and the SPD have a crushing majority in Parliament.
But after suffering a humiliating loss in September's elections, the SPD top brass have repeatedly said the party's role is now in the opposition. Its leader Martin Schulz has also said the party is ready for new elections.
Nevertheless, President Frank-Walter Steinmeier, who was a senior member of the SPD before becoming president earlier this year, could push the two together, citing national interest.
3 A MINORITY GOVERNMENT
Dr Merkel can also remain Chancellor but lead a minority government, as a candidate is elected to the post by parliamentarians. Such a minority government has also never been tested in post-war Germany.
The Bundestag can be called to vote up to three times. If she wins a majority of the votes, Dr Merkel could remain in office. But the veteran leader herself is not in favour of this high-risk option, saying that she wants a stable government.
And Dr Merkel's decision to meet President Steinmeier, who has the power to call a new election, signalled that she would not seek a minority government with the Greens after the Free Democratic Party pulled out of the talks.
4 NEW ELECTIONS?
A return to the ballot box in early 2018 is the most probable option. Before new elections could be called under Germany's Basic Law, the Bundestag Lower House of Parliament would have to be dissolved. Normally, the chancellor could trigger this by calling a confidence vote in Parliament.
Because Dr Merkel is only the head of a caretaker government, she does not have this option, but President Steinmeier could nominate her for election by the Bundestag. Following up to three rounds of voting, he would then have one week to decide whether to recognise Dr Merkel as chancellor or dissolve the Bundestag. If he chooses the latter, snap elections must be held within 60 days.
AGENCE FRANCE-PRESSE, REUTERS