By Fabrizio Romano
The Croatia international, 21, has impressed at San Siro over the last two-and-a-half seasons and is top of Rafa Benitez's wishlist as he looks to strengthen his midfield.
Los Blancos made an initial offer of €30m for the former Dinamo Zagreb starlet, which was rejected, but hope that the addition of €5m in bonuses can seal the deal, with Inter expected to accept the proposal at that price.
Kovacic, who would link up with countryman Luka Modric in the Madrid engine room, has already verbally agreed personal terms with the capital-city club as a switch nears completion and will sign a five-year contract worth €4m per season.
With five goals in 35 Serie A appearances last term, the midfielder caught the attention of many top sides this summer, with Liverpool reported to be interested in luring him to the Premier League.
The Nerazzurri had been adamant that the Croatian would not leave, while the player's agent has reiterated that stance, but the lure of Madrid has proven too strong.
Madrid have long sought a central midfielder, with the lack of reinforcements in that area exposed last season while Modric was injured, and Benitez has first-hand experience of Kovacic's talent thanks to his time in Serie A.
The Spanish coach had been linked with the likes of William Carvalho and Arturo Vidal this summer, the latter joining Bayern Munich, but appears to have finally found his man in Kovacic.
Inter are well set to deal with the departure of the 21-year-old, having already signed Geoffrey Kondogbia, though will look to reinvest the €35m fee in another midfielder, a striker and a left-back, while Madrid could be prepared to offload either Lucas Silva or Asier Illarramendi, who has been linked with Liverpool recently.