The SPD chief's comments have sparked backlash among his conservative coalition allies. European Parliament President Martin Schulz considered a possibility to succeed Frank-Walter Steinmeier.
Frank-Walter Steinmeier's nomination on Monday to become Germany's next president means that his foreign minister post will need to be filled.
The head of the Social Democratic Party (SPD), Sigmar Gabriel, insisted on Monday night that the position should go to a candidate from his party, rather than one from other coalition parties, the conservative Christian Democratic Union (CDU) or Christian Social Union (CSU).
"In any case that's how it's written in our coalition agreement [that the SPD has a right to the foreign minister candidacy]," Gabriel said on ZDF television, "and we will not be changing that."
The SPD leader did not name a potential successor: "I believe we should answer one question at a time," he said.
Reports suggest that European Parliament President Martin Schulz is the favorite to take over from Steinmeier. Jo Leinen, an SPD member of the European Parliament from Germany, told the news agency AFP that it was "very probable" that Schulz would switch Brussels for Berlin.
EP President Martin Schulz is "ideally suited" for the foreign minister position, according to allies.
Leinen added that Schulz would be "ideally suited" for the foreign minister position and prove a useful ally in Gabriel's quest to win next year's general election in Germany.
Internationally, Schulz is perhaps best known for his failed attempt to become president of the European Commission in 2014, standing as the chosen candidate for Europe's center-left alliance of parties. Because the center-right EPP alliance, including Merkel's German conservatives, won the most votes, their candidate Jean-Claude Juncker took the role.
After that vote, Schulz became party to a deal among the main groups in the European parliament, agreeing that he would remain as European Parliament president until early 2017, when he would hand over to an EPP member instead.
The EPP is expected to present a candidate on December 13 and has said that this deal remains unchanged, meaning Schulz would be seeking gainful employment.
Gabriel could face challenge over foreign minister post
The conservative CDU-CSU alliance, however, disputed Gabriel's claim that the next foreign minister should come from SPD ranks.
Jürgen Hardt, the Union's spokesman for foreign affairs, said that Steinmeier's successor should hail from the Union's ranks. The SPD, he believes, will struggle to find to a creditable candidate.
"What goes for the German president, namely that the role should fall to the best candidate, also goes for the foreign minister," Hardt told German online newspaper Zeit Online, seeking to reverse the argument used by the SPD for Steinmeier as president. Nobody else in the SPD could currently fill the position with the same clout as Steinmeier did, he said.
Senior Social Democrat Axel Schäfer saw the matter differently to Hardt, telling German news agency dpa that the SPD boasted a number of creditable candidates. Like Gabriel, he also referred to the coalition agreement - the deal reached between the CDU and SPD after 2013's elections and before jointly forming a government.
"To embark on speculation regarding coalition personnel some three months before the presidential vote in the Federal Assembly is dishonorable," he said.
dm/msh (dpa, AFP)