Schulz, 60, had been pushing for a third 30-month term as EU parliament president in defiance of a deal that he make way for a speaker from the center-right, the chamber's biggest group.
Should the conservatives, who have formed an effective grand coalition in Brussels with Schulz's center-left, claim the presidency in January, all three main EU political bodies would be headed by the center-right -- a possibility that has raised talk of change at the European Commission and European Council.
Commission President Jean-Claude Juncker had pressed his fellow conservatives in Parliament to let Schulz stay on in the interests of stability following Britain's vote in June to leave the bloc. He denied threatening to resign if Schulz were forced out but said on Thursday he "regretted" him leaving.
Juncker, from Luxembourg, has a five-year mandate running until October 2019. Council President Donald Tusk, the former Polish prime minister who will chair Brexit negotiations, has a 30-month mandate that expires in May.
He has broad support among member governments to stay on -- though not from his home country, where his opponents are now in power. He has not publicly stated whether he plans to continue.
The conservative leader in Parliament, Manfred Weber from Merkel's Bavarian allies, said his group would choose a nominee for speaker next month. Frenchman Alain Lamassoure and Mairead McGuinness of Ireland declared their candidacies.
Weber, 44, has been cited himself as Schulz's successor, a position that could raise his profile for a future career in Germany and something Schulz also used to his advantage.
Weber did not, however, rule out that his group might back a "consensus candidate" from another of the mainstream, pro-EU blocs in the chamber, which include liberals and greens. That could dampen complaints of a center-right lock on institutions while, as Weber said, maintaining a centrist front against the chamber's vocal minority of eurosceptic and extremist parties.
Weber's center-left counterpart said he would resist a conservative sweep of EU jobs: "A right-wing monopoly on the EU institutions would be unacceptable," said Italian Gianni Pittella. "Political balance must be ensured and respected."
Speculation that Schulz would return to German politics grew after Merkel's grand coalition with the Social Democrat SPD backed Schulz's party ally Steinmeier to take over in February as Germany's figurehead president. Senior SPD members see Schulz as the party's clear favourite to succeed Steinmeier.
Whoever takes over the role will have an overflowing in-tray as Germany tries to unite a divided post-Brexit EU, contain an assertive Russia and work out a new relationship with Washington under Donald Trump. Schulz has said
Trump's election as president will make work harder for the European Union. Opinion polls put Merkel in a very strong position to win a fourth term, despite a loss of support notably over her welcome for a million asylum seekers last year. The SPD trails badly but could end up in a new grand coalition under Merkel.
Apart from Schulz, the other leading figure to be the SPD's choice for chancellor is party leader and vice chancellor Sigmar Gabriel. An poll this week showed Germans thought Schulz would have a somewhat stronger chance than Gabriel of ousting Merkel.
A member of the SPD leadership told Reuters on Thursday that it would decide between Schulz and Gabriel by late January.
Schulz ran a bookshop in his native Aachen in western Germany before entering the European Parliament in 1994. As speaker of the body since 2012, he used new powers granted by the 2009 Lisbon Treaty to increase the legislature's role in EU politics and has used the post to raise his profile at home.