After scoring the first of his three goals in a thrashing of Paderborn on Sunday, Sancho revealed a t-shirt bearing the handwritten message "justice for George Floyd", for which he received a booking, with team-mate Achraf Hakimi also revealing a similar message.
Sancho's tribute followed on from Thuram taking a knee after scoring for Borussia Monchengladbach against Union Berlin, while Schalke's United States international McKennie wore a "justice for George Floyd" armband.
Floyd died while in police custody in Minnesota last week, sparking large scale protests and riots in many cities in the United States.
DFB control committee chairman Anton Nachreiner has now confirmed the tributes are to be looked into, stating: "The DFB control body will attend to this issue in the coming days and scrutinize the circumstances of the case."
According to DFB regulations, such statements are prohibited.
Following Dortmund's 6-0 victory at Paderborn, England international Sancho - on the back of his first professional hat-trick, tweeted it was a "bittersweet moment".
Meanwhile, Gladbach coach Marco Rose lauded Thuram for his celebration, insisting the Frenchman had "set an example against racism".