German Chancellor Angela Merkel appeared optimistic on Sunday that despite major policy differences – her Christian Democratic Party (CDU), the Greens and the pro-business Free Democrats (FDP) were only days away from a preliminary coalition agreement.

"In my opinion, with some good will we can achieve a solution," the chancellor said, adding with characteristic pragmatism that "if that's the case, we'll see anyway by the end of the week."

The three parties are set to publish their initial coalition agreement on Thursday, nearly two months after Germany's general election and four weeks since the negotiations began.

Should they succeed, talks would go into their final phase of settling on an official coalition contract that would set the country's political agenda for the next four years.

Uncharted three-party territory

But three parties in a coalition is unwieldy and uncharted territory for Germany. Many sticking points remain on topics from taxes to climate change to refugee policy. The latter is particularly tricky as there are divisions not only between the Greens and the FDP, but even between Chancellor Merkel and the CDU's Bavarian sister party, the CSU.

CSU leader Horst Seehofer made no secret during the 2015 refugee crisis that he did not appreciate Merkel's open-door policy, and has reportedly told Merkel – who has moved the CDU too far to the middle for the CSU's liking – to stick to a more conservative immigration strategy in the future if she wants the CSU's unconditional backing.

Watch video 11:28 Morning Q&A: Coalition talks – Reinhard Schlinkert

FDP leader: Talks may fail

Reports of the rough road to compromise have not been helped by FDP leader Christian Lindner, who said last week that he saw a "50-50 chance" of the coalition talks collapsing, which could potentially trigger fresh elections.

"The chances are 50-50, and whether the odds get a bit longer or shorter is something we'll see at the end of this week or the next," said Lindner. "We don't want a new election, but we're not afraid of the voters."

After failing for the first time to reach the 5 percent hurdle to enter the Bundestag in 2013, the FDP leader may feel he has something to prove, but the Green party has warned that talk of fresh elections is irresponsible.

Months of talks

Due in part to Germany's Nazi past, politicians are willing to go to great lengths to avoid forming a minority government. So after the CDU's disappointing 32.9 percent finish in the elections on September 24, the party needs the FDP and the Greens in order to represent over 50 percent of voters.

However, even if an initial coalition agreement doesn't materialize this week, it wouldn't necessarily induce any hand-wringing – in 2013, the CDU and center-left Social Democrats (SPD), took over two months of coalition talks before agreeing on the terms of the so-called "grand coalition" of the country's two biggest parties.