Last night's exploratory talks dragged on nearly 24 hours because of disagreements on refugee policy and reform of the tax, pension and health systems. The heads of the coalition parties also ruled out the tax increases earlier demanded by the SDP.
Merkel had earlier warned that the leaders faced a hard round of talks to try to end negotiations on Thursday.
"We have felt since the elections that the world will not wait for us, and in particular. we are convinced we need a new call for Europe", Dr Merkel, who has played a central role in tackling crises over the euro and refugees, said after exploratory talks that had run through the night.
If the SPD delegates give the thumbs up, formal coalition talks could in theory begin as soon as January 22.
German President Frank-Walter Steinmeier reminded the negotiators of their responsibility - towards not just their own parties and political futures, but also to?Europe.
Despite such reticence, German media reported on Tuesday that conservative and SPD negotiators had reached agreement on a law to attract skilled immigrants. The preamble to 28-page document born of a strenuous negotiating week announces "a new beginning for Europe", as a priority of "new political time".
Merkel acknowledged there are no guarantees this proposed deal will ultimately be adopted.
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The coalition destroyed a boat carrying explosives as it headed toward the tanker on Saturday, coalition spokesman Colonel Turki al-Maliki said.
But it has shown itself to be reluctant to team up again with the chancellor after suffering a humiliating defeat in the elections.
The new Merkel-led government will seek to "strengthen social cohesion in our country and overcome the divisions that have arisen", the paper says following September's inconclusive election when both the conservatives and the SPD suffered a big slump in support.
When the Free Democrats unexpectedly backed out, Merkel had to go to plan B: a revival of the grand coalition between the center-right and the center-left that has governed Europe's largest economy for the past four years.
"But the biggest hurdle is probably the refugee policy, because the conservatives are very anxious that if they don't tighten this, that more voters are going to go to the Alternative for Germany party, which is a far-right party that is now in parliament".
After the parties cleared obstacles on immigration and taxes, Merkel said she was "optimistic" they could seal a deal on a "stable" right-left "grand coalition" government.
A survey published by the Bild newspaper in late December showed that almost half the country did not want her to complete a fourth term.
Published by the business daily Handelsblatt on Thursday, the poll found that 56% see Merkel departing early.
Also, the deal avoids the risk of another election, which would have raised the prospect of more gains by populist parties such as the far-right AfD.
Party officials believe a new government is unlikely to take the reins of power until possibly April.