Los Blancos are hoping to have the 19-year-old in place for their LaLiga opener against Espanyol on August 22nd - but the Spanish giants are against the clock at this stage.
Real Madrid have seen off competition from rivals Liverpool and PSG for Diomande, but their final barrier is Leipzig themselves, as the Bundesliga outfit push for as high a price as possible in the negotiations.
The 19-year-old is under contract until 2030 in Leipzig, so his current club want to make a major profit, after signing him from Leganes for just over €20M last summer.
As per the latest from The Athletic, RB Lepizig have made an internal decision not to include him in any of their preseason games, to guard against a possible injury.
They have also informed Real Madrid of a final asking price set at €130M (£111M) which is above their most recent offer.