Without naming the man, a spokesman for police in Hagen, a west German town just south of Dortmund, said complaints against him had been made in recent days.
Dortmund had earlier this month urged anyone who could give information on sexual abuse at the Bundesliga club to come forward after the Bild newspaper reported internal concerns that an unnamed former manager had abused a youth team player.
Citing a lawyer's letter and five-page dossier passed over to the club in 2010, Bild reported that an alleged victim had accused the manager of linking professional success to sexual favours as well as touching him inappropriately and attempting to kiss him.
Responding to the allegations, Dortmund said in a statement it had received complaints about the alleged abuser in 2010 and then again in 2023 before dismissing him from an unspecified but minor position and "ensuring that he left the club".
The 2023 complaint, also reported on by Bild, concerned alleged incidents that did not involve others connected with the club, Dortmund said, adding that the man denied the allegations.
In a later report, Bild said it had so far spoken to eight accusers - including former fans, youth players and neighbours of the man - with the youngest said to be 11 at the time of the alleged abuse.
The incidents concerned are said to have taken place decades ago.
Borussia Dortmund told AFP that it had instructed external investigators to look into the allegations and said that it would provide them with "all available means".
"We further encourage all victims of interpersonal and sexual violence, as well as anyone who can provide information about such incidents, to use the whistleblowing systems," it added.