Currently on-loan at RBL from PSG, Simons can sign permanently for a fee rising to €80m.
Red Bull football chief Klopp is tasked with keeping Simons with Leipzig, but any chance of an outright deal is dependent on Champions League qualification.
Also interested in the Holland international are Barcelona, Inter Milan and Klopp's former club, Liverpool.
It's been suggested Klopp is attempting to renegotiate the fee terms, with a suggestion of €50m up front plus €30m in resale now being tentatively proposed.