They reportedly made some progress Saturday on finding common ground and were pushing for an agreement later Sunday.
Incumbent chancellor Angela Merkel's only realistic hope of securing a fourth term after suffering losses in September's election is an awkward three-way conservative-liberal-Green alliance.
While billed as exploratory, the talks have been so hard-fought because once the parties agree to start working on a formal coalition pact and cabinet assignments, "there's no turning back", Bavarian premier Horst Seehofer, who is negotiating for the Merkel-allied Christian Social Union, told reporters.
FDP leader Christian Lindner said the talks now had to be wrapped up by 5 p.m. GMT on Sunday.
The biggest sticking points are climate change, where the Green Party wants emissions cuts that the other parties see as economically ruinous, and immigration, where Ms Merkel's arch-conservative allies in Bavaria insist on stricter rules.
German President Frank-Walter Steinmeier called on all sides to stop jockeying for position and move forward.
After four weeks of preliminary talks, negotiators said Saturday that consensus on economic policy, Europe and transportation are within reach.
"Before they get going there are always attempts by parties to drive prices up as high as possible", he told Welt am Sonntag.
Among its demands are a cap of 200,000 per year on the number of refugees Germany will take, and an end to the practice of allowing successful asylum seekers to bring their immediate families to join them. "In many ways, what we've witnessed in recent weeks isn't much different from earlier coalition negotiations".
But the heterogeneous three-way coalition, made necessary after the conservatives and the center-left suffered punishing election losses, is nearly without precedent in Germany's post-war history. The three factions - nicknamed Jamaica for their respective party colours - haven't governed together at the national level, and post-World War II Germany has never held a repeat election.