Dani Ceballos, 20, starred as part of the Spain team that reached the final of the European Under-21 Championship in Poland last month, where he was named player of the tournament.
The midfielder was also linked to Barcelona but Madrid appear to have beaten their rivals to get their man, with Haro confirming his club are in talks with the LaLiga champions to bring the transfer to a conclusion.
“Dani has rejected our offer to extend his contract with Betis and Real Madrid have told us that he has an agreement with them,” he said.
“Both clubs are talking, in hours or days we will have news.”
Madrid are reportedly eyeing a deal worth in the region of €18million for Ceballos, who is expected to sign a six-year contract.