The parties' leaders will meet at Steinmeier's official residence in Berlin to discuss "the situation after the breakdown of the coalition talks".
German Chancellor Angela Merkel has rejected new elections and wanted to form a new government quickly, as a outcome of the failed government coalition talks with the Free Democratic Party (FDP) and the Greens.
Horst Seehofer, the Bavarian prime minister and head of the CSU, said an alliance with the SPD was "the best option for Germany".
A new election will have to be called if no government can be formed.
European leaders have stressed the importance of Germany getting its political house in order ahead of the European Council summit in December.
Merkel, who has baulked at the idea of a repeat election, on Saturday said she wanted to form a government "very soon".
Chancellor Angela Merkel faced pressure from inside her conservative bloc Sunday to aim for a quick coalition deal with center-left rivals without conceding too much ground on core issues such as immigration. The Greens have said they are open to a minority government.
"We worked well together", she said, adding under the grand coalition, Germany enjoyed the strongest labor market for decades, a balanced budget and pensioners and families had benefited, she argued. Leading SPD figures have outlined conditions including investment in education and homes, changes in health insurance and no cap on asylum seekers.
"If there is a grand coalition or even if there is toleration (of a minority government) I would expect more emphasis on the SPD's program", Clemens Fuest, president of the Ifo institute, told business newspaper Handelsblatt. "There shouldn't be a grand coalition at any price".More news: Google promises to stop collecting Android location data after being caught