According to the aforementioned source, Premier League pair Chelsea and Tottenham both submitted offers of €150m for Asensio last summer, only for Real to reject their proposal out of hand.
"If anyone wants the man from Mallorca, he will cost them €700m," insisted Real Madrid president Florentino Perez, thought to be one of Asensio's biggest fans.
Perez is thought to see the young playmaker as a vital component of Real Madrid's future and whilst he hasn't featured as often as he would have liked so far this campaign, Real boss Zinedine Zidane turned to the former Real Mallorca man at a key time during Wednesday night's Champions League victory over PSG, with Asensio answering the call and then some.
In his first seven minutes on the pitch the 22-year-old laid on two assists to help Real claim a huge win, with PSG having previously appeared the most likely to take the advantage ahead of the second leg in Paris.
Despite being up against two right-backs in the shape of Thomas Menuier and Dani Alves, Asensio once again showed his precocious talent to pick the French side apart and put Real in the driving seat.
Though his game time has been limited under Zidane, the Frenchman has always been a fan of Asensio, with his message to the youngster an emphatic: "Be pacient Marco."
Wednesday night's game was the latest demonstration of Asensio's abilities and a reminder as to why Real reportedly rejected such big offers for the playmaker.