The Gunners have been heavily linked with the 21-year-old for some time, amid talk that Arsene Wenger has made bolstering his striking options a priority for the coming months.
Los Blancos are aware that their youngster is seeking a switch away from the club in search of regular action after spending last season battling with youngster Jese as Karim Benzema’s back-up.
Arsenal were thought to be looking to get Morata in for a reduced figure given the situation, but Real are demanding £24m.
The Champions League winners are aware that their starlet is one of the continent’s top emerging goal-getters, and are loathe to lose him for a small fee.
However they will drop their demands to between £14m-£20m if a buy-back clause is put into the deal to allow them to bring Morata back for 30% more than the fee they receive for him within the next two years.
It is understood that the La Liga side will pursue Christian Benteke of Aston Villa or Chelsea’s Romelu Lukaku if they do sell.