According to Der Spiegel, Hamburg's state prosecutors' office are investigating Martin Ott, Facebook's managing director for Northern, Central and Eastern Europe.
Prosecutors said last month that they were investigating three Facebook Germany GmbH managers to decide whether to press charges.
A complaint had been filed by Bavarian lawyer Chan-jo Jun against the managers, pointing in particular to examples of hate speech and racism related to refugees, including posts that show Nazi symbols like swastikas and Hitler salutes, according to Die Welt.
It was the first time that Facebook managers have been targeted over hate comments on the site.
Under the German criminal code, the crime of incitement of hatred is punishable of up to five years in prison for encouraging violence or hatred towards others for their religious, racial or ethnic background.
Written comments are punishable with up to three years in prison, including those who disseminate them or make them accessible.
Facebook under fire
Spiegel reported that in his position, Ott is ultimately responsible for whether hateful comments are deleted.
Facebook has faced tough scrutiny in Germany for not doing enough to monitor hate speech on its network, particularly amid the refugee crisis.
Facebook founder Mark Zuckerberg told Chancellor Angela Merkel recently that the company would do more to combat racist comments.
Prosecutors must still determine whether there is enough evidence to press charges against the executives.
Though Facebook did not comment directly on the investigations, Spiegel reported that a spokesperson did say: "It is for us important to point out that there are various ways to report content on Facebook."
Germans adrift in an online ocean
Klemens Skibicki, Director of the Institute for Law and Communications on the Internet at the Cologne Business School, told The Local that the case was yet another example of German and American views of free expression clashing online.
Americans value free speech above all else, but are more prudish than Germans when it comes to nudity, for example.
"It appears almost impossible to respect every different cultural point of view amidst the unimaginable volumes of data [on Facebook]," Skibicki said, pointing out that Germans are just 30 million of the social network's 1.5 billion users.
Facebook bases its actions on its American terms of service and Irish law (given that its European HQ is in Ireland), he explained.
"It will in any case be exciting to see how the networked cultural space of the Facebook generation will develop," Skibicki added.
"My prediction is that for the probably very few cases which represent a criminal action, those involved will find a way through, with the involvement of the justice system, that will see Germans on Facebook having to bear things just as if they were sitting around a pub table."