Nahles still needs to be formally nominated by the party executive, which is meeting on Tuesday evening.
Nahles, 47, shot to national political fame during the fraught days of the last SPD government 15 years ago when, as a left-wing lawmaker, she helped lead a party rebellion against its tough social reforms.
Schulz has been plagued with criticism from within the SPD, especially the youth branch of the party who have been vehemently against a coalition deal with Merkel. The party's 464,000 party members will vote in a postal ballot on the deal, with the results expected to be announced on March 2.
The most urgent matter for the SPD is to get a new leader in place after Martin Schulz said last week he would quit to allow the party to regroup.
"With my resignation from office and decision not to participate in the government, I want to bring the personnel debate in the SPD to an end so that the members can really concentrate on what is in the coalition agreement", Schulz told reporters.
Just 33 percent of German citizens said the SPD would be more successful under Nahles, while 52 percent did not expect this to be the case.
The development followed Schulz's announcement Friday that he was abandoning plans to become foreign minister in the new government.
Tensions are also reported between him and Sigmar Gabriel, an SPD colleague who is now foreign minister.
The SPD's turmoil broke into the open again Tuesday over the question of Schulz's successor.
Many in the SPD fear that re-entering a coalition with Mrs Merkel's Christian Democrats (CDU) and the Bavarian CSU could damage the party in the long term.
Germany has been without a formal government since the September 24 election as Merkel failed to form an alliance with two smaller parties.
Michael Fuchs, a former member of parliament with Merkel's Christian Democratic Party (CDU), said he is optimistic that Germany's finances will continue to be run efficiently. The far-right populist Alternative for Germany (AfD) entered the Bundestag for the first time. Social Democrats from Schleswig-Holstein, Berlin, and Saxony-Anhalt have hinted that any one of Schulz' six former deputies could become the next SPD leader.
Nahles said that she would start campaigning at the weekend for members to approve the coalition agreement with Merkel.
The SPD originally wanted to reinvent itself in opposition but reconsidered when Merkel's attempt to form an alliance with two smaller parties failed late previous year.