Klopp, who was appointed as Red Bull's head of worldwide football after his departure from Liverpool at the end of last season, would be a big fan of the Spaniard.
According to Fabrizio Romano, the German Fabregas would like to be the permanent replacement for Marco Rose after his resignation in March.
Fabregas is impressed by the Italian side Como and brings them to the tenth in the Serie A with only just earned promotion.
It is understood that the former midfielder of Chelsea and Arsenal still has to decide on his future, despite the fact that Klopp makes personal contact with him.
Romano said: “Klopp had direct contact with Cesc Fabregas a few weeks ago to talk about the Leipzig project. Cesc decides to stay in Como, that is the position of the coach.”