The 21-year-old, who scored the fourth goal inearlier this week, had been earning plaudits for his recent performances and Liverpool have apparently been impressed by what they’ve seen.
According to the report, the reigning European champions have rejected the offer as they are keen to keep hold of the youngster.
Madrid are willing to let James Rodriguez leave in the summer, partly because they want to give Asensio more time to develop in the first-team.
Real paid around €4million to sign the Spanish international from Mallorca back in 2014, but they allowed him to stay on loan there for the remainder of the season.
He spent the 2015/16 season on loan with Espanyol where he showed flashes of his ability and Zinedine Zidane decided to keep him for the current campaign.