The highly rated 18-year-old has been heavily linked with both Real and their arch rivals Barcelona, while Premier League giants Manchester United were also said to be interested.
But it appears Real have won the race for his signature, with reports indicating that they will pay Segunda side Mallorca a fee in the region of €3.7 million to secure Asensio's services on a five-year-deal.
Real coach Ancelotti said on Monday: "Asensio is a good player and we will try to have him by our side this summer, but not in January."
While the transfer, which will allegedly see Asensio return to Mallorca on loan next season, is yet to be made official, the player has already spoken of his delight at agreeing a switch to the European champions.
"I've decided to go to Real Madrid and I'm very happy," Asensio told Cadena SER. "I'm proud that big clubs watch me and Real Madrid is the best club. The agreement is for five seasons, it's a moment to savour.
"I'm keen to seal the deal so we can all relax, the club, me and Real Madrid."
Asensio has made 14 league appearances for Mallorca this season, scoring three goals for a side that sits 13th in the Spanish second tier.
