The Serbian forwards future has been the centre of intense speculation in recent months, with Madrid repeatedly among those clubs in conversation with a player who has been in imperious form this season.
Jovic has netted 25 goals in all competitions, in what is the final season of his two-year loan deal from parent club Benfica.
With the season set to draw to a close for both the Bundesliga and La Liga outfits this weekend, AS claim that Los Blancos will finalise the deal after the weekend with an agreement in place for Jovic to join the Spanish giants.
Madrid are required to cough up a fee in the region of €60m for the prolific striker, however, giving the spending power of Zinedine Zidanes men, this is not expected to be a problem.
After Marianos disappointing return to the club after a spell at Lyon, Karim Benzema continues to remain the clubs only reliable frontman, with Jovic expected to provide serious competition for the 31-year-old.
Ten years his senior, AS state that the 21-year-old is the perfect replacement for the Frenchman, and will eventually take over the mantle as leading striker.
Eintrachts domestic season is not done and dusted yet, with the German side fighting to earn a top four spot - something that is more than achievable with just one match remaining. Die Adler are currently sixth, but just one point off fourth place Borussia Mönchengladbach ahead of their away trip to Bayern Munich.