But the three parties have clashed over immigration, Europe and finance.
The CDU and the SPD began talks on a grand coalition after negotiations for a so-called Jamaica coalition, between the CDU, the Free Democrats, and the Green Party, collapsed previous year.
Commenting on the current political situation in the country, German President Frank-Walter Steinmeier said that "we are now facing a situation that has never happened before in the history of the Federal Republic of Germany, that is for nearly 70 years".
Every political career ends, and Merkel's finale may be coming faster than just about anyone had predicted.
"It would be the end for all three if this coalition does not come about", said Karl-Rudolf Korte of Duisburg-Essen University.
As Germany struggled to emerge from a 4th month of political paralysis, its economic health stood in stark contrast.
CDU-CSU and SPD leaders are due to report to their party executives on the outcome of the talks on Friday morning.
The Social Democrats reportedly received commitments for hiring more care workers and increasing salaries in the sector, and for no cuts to the minimum pension level until at least 2025.
The conservatives baulk at tax hikes.
According to German Press Agency, the SPD board voted by a large majority for coalition negotiations, and the CDU board and the CSU regional group approved unanimously.
All three lost votes and seats in the September 24 elections, making the Social Democrats, in particular, reluctant to resume that arrangement.
For the deal, Schulz said Friday he had the unanimous endorsement of the SPD's negotiating team, but he still needed clearance from a party conference to be held in Bonn on January 21. In reality, the next "grand coalition" wouldn't be up and running before the beginning of April. "That s why I think we have a good chance", said Kuehnert.
Despite the agreement, potential pitfalls remain, including upcoming votes by sceptical SPD delegates and members that could yet derail plans for another left-right "grand coalition" - the constellation that has ruled Germany for the past four years and remains in charge as a caretaker government.
A grand coalition would also leave the controversial Alternative for Germany as the lead opposition party in parliament.
After all, there is little appetite for a new conservative-SPD alliance.
The chancellor, who commands wide respect overseas after more than 12 years in power, needs coalition talks to succeed to avoid further erosion of her personal authority and Germany's worldwide influence, not least in the EU.
Another poll, published by public broadcaster ARD, found that only 45 percent viewed a new GroKo positively, while 52 percent did not.