According to Sky Germany, the Spanish giants submitted a written offer worth 100 million euros. The proposal included a guaranteed 90 million euros, with a further 10 million euros in performance-related add-ons.
Leipzig, however, rejected the bid, just as they did with Liverpool's earlier offer of the same value.
The Bundesliga club remain firm in their valuation of the defender and are not willing to negotiate at the current price.
Paris Saint-Germain are also interested in signing Diomande, although the French champions have not yet made an official offer. Reports suggest there has only been contact between PSG president Nasser Al-Khelaifi and Leipzig executive Oliver Mintzlaff.
The 19-year-old Diomande is believed to have agreed personal terms with PSG on a contract that would keep him at the club until 2031, but that agreement has not changed Leipzig's stance.
The German club are determined to keep hold of one of their prized assets unless they receive what they consider to be an extraordinary transfer fee.
Should Real Madrid decide to return with an improved offer, PSG could face a major challenge in completing the signing of the sought-after defender.
Real Madrid are increasingly confident they can sign Manchester City midfielder Rodri before the transfer window closes, with the Spain international emerging as one of the club's top priorities.
Jurgen Klopp has been confirmed as Germany's new head coach, signing a contract that will keep him in charge until 2030 as the German Football Association looks to restore the national team's place among the world's best.
Ermedin Demirovic could be set for a move away from VfB Stuttgart this transfer window, with Juventus, Fenerbahce and Leeds United all reportedly interested in signing the Bosnia and Herzegovina striker.
Barcelona have confirmed that midfielder Frenkie de Jong will be sidelined for several weeks after suffering a tear to the medial collateral ligament (MCL) in his right knee.
