A detailed report by the Süddeutsche Zeitung says some inside the DFB felt they had been "caught off guard" by the 55-year-old's activities.
According to the report, the association's supervisory board received "no detailed information" about Kosicke's exact areas of responsibility, fuelling fears that conflicts of interest could arise.
Klopp brought Kosicke with him to the DFB as an adviser after taking over as coach of the Germany national team. The two already knew each other from Kosicke's work as a manager at sportswear manufacturer Nike in the early 2000s.
Still, Kosicke's exact role has not been clearly defined. While association president Bernd Neuendorf called him an "external employee", the DFB described the 55-year-old in a statement as an "external adviser". Klopp, meanwhile, said at his introductory press conference that Kosicke was his "assistant coach for strategy, development and innovation."
IMAGOIs Jürgen Klopp's adviser becoming a "problem appointment" for the DFB?
What Klopp's right-hand man actually does also remains unclear to many inside the DFB, according to the SZ. On top of that, his numerous secondary roles could turn the 55-year-old into a genuine "problem appointment" for the DFB. There is talk of "growing irritation".
Kosicke's professional ties across football are extensive. Research by the SZ says he remains a shareholder in Onside Sports GmbH, which specialises in organising friendlies and training camps. It is also claimed his links to Projekt b, the company he founded that manages sporting directors and coaches, were not disclosed to the DFB.
He was also involved in the marketing agency projectFIVE, although he recently said he had had "no shares there for a year and a half". He continues to run Projekt b, but is focusing "exclusively on advising the DFB".
There are apparently broader fears that, through his network, Kosicke could gain too much influence over the DFB's decision-making levels and create conflicts of interest. According to president Neuendorf, the 55-year-old has "open doors right up to my presidential office".
Getty ImagesUli Hoeneß voices clear criticism of the DFB's decision
Uli Hoeneß had already criticised the German association's decision to bring Kosicke into the DFB as Klopp's adviser. The Bayern Munich club patron described it as a "friendly takeover" by "Klopp and Co."
"What I don't like about the whole thing is that his adviser Marc Kosicke was bought in as well. I don't know exactly what he is supposed to do there. I think that is a problem," said Hoeneß.
Klopp then defended his confidant: "With me, most people perhaps tend to give me a bit of the benefit of the doubt. And Marc is looked at a bit critically because the role didn't exist. Before we started, people were still saying: 'You can't just change the coach.' So we don't just change the coach and then they say: 'Well, that wouldn't have been necessary either.'"
More broadly, he said he understood it all "completely. It's all fine. People are judging things before we've done anything at all."