For the conservatives, the Linke are just as unpalatable as the far-right Alternative for Germany, whom all major parties have pledged to keep out of government.
Scholz has made it clear that the Greens are his preferred partners, but the conservatives say he will need a third party to form a coalition government. And they say the Social Democrats are closer to the Linke on social policies than to the pro-business Free Democrats - the conservatives' preferred dance partner.
Few expect this to happen - the Linke are on just 6% in polls, half the liberals' 11%, which probably would not be enough to give Scholz the required parliamentary majority.
But for some investors, it is a risk that should not be overlooked.
"Inclusion of the Linke in a governing coalition would, in our minds, represent the single biggest wild card by far for financial markets from the German elections," said Sassan Ghahramani, chief executive of U.S.-based SGH Macro Advisors, which advises hedge funds.
Linke policies such as a rent cap and property taxes for millionaires would be enough to spook many in Germany's business class.
Most assume that a victorious Scholz - a strait-laced finance minister and a former mayor of Hamburg - would include the Free Democrats as a moderating influence in his coalition.
Both SPD and Greens have also ruled out working with any party refusing to commit to the NATO military alliance or Germany's European Union membership, both of which the Linke has called into question.
READY FOR GOVERNMENT
Undeterred, the leftists are pitching themselves as ready for government responsibility three decades after East Germany vanished from the map.
"We're already in NATO," party co-leader Dietmar Bartsch told a recent news conference, dodging questions over whether its foreign policy views would keep it from entering government.
Bartsch, 63, whose political career started when he joined East Germany's Socialist Unity Party in 1977, leads the Linke alongside Janine Wissler, 40, a westerner who hails from a town just outside Germany's financial capital Frankfurt.
If foreign policy is an obstacle, the party prefers to talk economics. Here it is not far from the Social Democrats or Greens and Bartsch says once in government the party would make sure its partners delivered on campaign promises, such as the SPD's proposed 12 euro hourly minimum wage.
The party has outgrown its East German base, establishing strongholds in poorer, post-industrial cities in western Germany.
It heads the government in the eastern state of Thuringia, and is the junior partner with the SPD and Greens in Berlin's city government.
Analysts say that, as a centrist, Scholz would be more comfortable with the Free Democrats, but will not rule out the Linke to keep leverage over the liberals, keen to play kingmakers in coalition talks.
The Social Democrats' lead in the polls also suggests the left's communist roots carry less weight with voters than in the past. Greens leader Annalena Baerbock said it was just wrong to say they were just as bad as the far-right because the latter did not respect Germany's democratic norms.
"I consider this equation of the AfD with the Left to be extremely dangerous, especially because it absolutely trivialises the fact that the AfD is not aligned with the constitution," Baerbock said in a television debate this month.
(Additional reporting by Paul Carrel; Editing by Tomasz Janowski and Alex Richardson) ((email@example.com; @tomescritt; +49 30 2201 33579;))