The bearded 60-year-old German former bookshop owner has been in office for five years, more than anyone else since the parliament held its first international elections in 1979.
Schulz now looks set to seek another two and a half years at the helm of the EU's only elected body, a position whose profile he has raised with outspoken views on issues ranging from Brexit to Grexit.
But Schulz will be ignoring a deal between right and left-wing parties – which he himself signed on behalf of the Socialist group – stipulating the presidency should alternate between the political camps every 30 months.
Right-wing parties are demanding Schulz honour this commitment come January 2017.
“We have an agreement with the Socialists – Martin Schulz signed it himself,” said an MEP from the EPP group, which brings together the main conservative parties in Europe.
“If he puts himself forward again, he would be declaring war.”
'We need stability'
Schulz has already won the support of the leader of the Socialist group in the European Parliament, Gianni Pittella, who has spoken out in favour of a new mandate for Schulz, as has the German vice chancellor, Sigmar Gabriel.
More surprisingly, in July Schulz received the support of European Commission President Jean-Claude Juncker – himself a leading member of the EPP and the man who beat Schulz to the Commission job
“I am in favour of the European institutions being led for the next two-and-a-half years as they have been thus far. We need stability,” Juncker told German newspaper Der Spiegel when asked about the parliament presidency in a joint-interview with… Martin Schulz.
At the end of his first term Schulz was re-elected in July 2014 for another two-and-a-half year mandate with support from right-wing and centrist voters.
The EPP however insists Schulz is far from indispensable – while also criticising him for failing to publicly state that he wants to stay on in the job.
“For months, without ever saying anything himself, all sorts of people have been saying that he's just that good that we won't be able to survive without him,” an influential EPP politician said mockingly.
Run against Merkel?
Potential successors floated by the conservatives include former French minister Alain Lamassoure, the former European commissioner Antonio Tajani, an Italian close to Silvio Berlusconi, and the Irish MEP Mairead McGuinness.
If he does decide to seek a new mandate, Schulz will be starting off on the wrong foot, seeing as he would have to convince a fair few MEPs outside of his own political circle.
Despite this, Schulz has been praised for bringing the role on to the world stage, although he has also ruffled a few feathers with his “autocratic style”, says the German Green politician Reinhard Bütikofer.
“He's had his time. We won't support him,” said the French ecologist MEP Michele Rivasi.
German media say Schulz is already considering a plan B: a political career in Berlin.
It has been suggested that he might take on Angela Merkel in next year's elections.
On this, Schulz has only said that Sigmar Gabriel is the “legitimate candidate” of the Social Democratic party – pointedly failing to rule out a run himself.