Real see the 21-year-old as having a bright future at the Bernabeu, and have set an asking price of around £40million, the newspaper reports. The midfielder already has two caps for the Spanish senior side after making his debut in a friendly match against Switzerland in the build up to Euro 2016 last May.
So far this campaign, Asensio has had his chances of first team football limited. He has featured 23 times in all competitions under Real boss Zinedine Zidane this season but has mostly been used from the bench.
Most of his game time has been in the Copa Del Rey where he has made six appearances so far. He has scored three goals and provided one assist in the competition, while in the league he has also scored twice.