The results will be announced on March 4, according to party officials.
Many grassroots members of the centre-left party are sceptical about another tie-up with the conservatives after serving in a similar coalition in 2013-17. Schulz had said shortly after the election last September that he wouldn't join another grand coalition, insisting the party would instead now "renew itself" in opposition.
The job is now held by Sigmar Gabriel, who handed the party leadership to Mr Schulz a year ago and has become one of Germany's most popular politicians since taking on the role of foreign minister.
The shock announcement comes just days after Merkel's conservatives and the SPD agreed to form a coalition government. The SPD lost 40 seats as its...
"This is a renewal in every way", said Stephan Weil, the SPD premier of the central German state of Lower Saxony, saying Nahles stood for a change in generation after SPD'sÂ current chief Martin Schulz announced on Wednesday that he was standing down to make way for her.
"I hereby renounce joining the federal government and at the same time implore that this should be an end to debates about personalities" within the Social Democratic Party (SPD), Mr Schulz said in a statement.More news: Arsenal 5-1 Everton: Premier League highlights and recap
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Chancellor Angela Merkel receives Valentine's Day flowers from the Central Gardening Association at the Chancellery in Berlin, Germany, February 9, 2018.
Sigmar Gabriel, a popular foreign minister in the previous government and until recently seen as a close friend of Schulz, bitterly attacked his party leader in an interview on Thursday, hinting at broken promises. A "no" vote would mean Germany would nearly certainly face. In addition to the controversy over Schulz, Merkel herself has been under fire for giving key ministries to the SPD to extend her 12-year reign over Europe's biggest economy.
Kuehnert, 28, is travelling around the country urging members to vote against a "grand coalition".
The deal will now be submitted to a ballot of the Social Democrats' membership, a process that will take a few weeks.
The SPD's traditional left-wing youth organization, Jusos, have opposed a coalition government with the Christian Democrats, and called for reform within the party.
The chancellor, who long seemed impervious to criticism from within her own ranks, has faced a barrage of complaints since Wednesday's agreement, which left her bloc with six ministers - the same number as the SPD, which fared considerably worse in September's national election.