However Fringer, who managed Di Matteo as a player at Swiss club FC Schaffhausen, believes that a move to Germany would not be right for him.
"I can assure all German clubs - if he comes to Germany, he will not suit this type of football," Fringer told Goal.com.
"I do think that he could help Schalke. But, I'm not convinced that he would pass [the opportunity].
"There are just clubs who always want too much and destroy everything with it, like Schalke. He is far too sensible and he knows that he could be put on the ejection seat. I do not think he would do it."
Di Matteo won the FA Cup and Champions League with Chelsea last season.