Raiola was accused of insulting a number of University of Wisconsin band members during their performance before Sunday's match between the Lions and the Green Bay Packers.
Schwartz has confirmed that he will look further into the allegations in the coming days and admits that he would be disappointed in his player should they prove to be true.
"When you go on the road, there's hostile environments, fans say a lot of things and stuff like that. We need to stay above stuff like that. I didn't hear that personally on the field. No other coaches did," Schwartz told reporters.
"I think we've already released a statement that we are going to look into it as an organization. I would be very disappointed if that was the case, because that's certainly not the character we want to display."
The Lions' statement also confirmed that they will look into the incident before taking action against Raiola.
"We are aware of the reports involving Dominic Raiola and the University of Wisconsin Marching Band," read the statement.
"Those reports are extremely inconsistent with the standard of behaviour we expect from our players and from every member of our organization. We currently are gathering more information and will respond further when appropriate."
The Lions went on to lose the game 22-9 to leave their season record at 3-2.