The LaLiga outfit will hold elections in March 2021.
Farre is hoping to defeat incumbent, Josep Bartomeu, who is coming to the end of his second term.
If he is elected, Farre is hoping to bring in Klopp, despite the fact Barca only replace Quique Setien with Ronald Koeman last week.
Asked whether he would keep Koeman in charge, Farre told Sport: “If Koeman works and does well, I would, of course.
“Obviously, we have our roadmap and we had already had several conversations with Jurgen Klopp, because it seems to us that Barcelona needs such a coach.”