The Gunners were heavily linked with a temporary swoop for the Spaniard over the summer, but saw their efforts thwarted as the La Liga giants opted to keep the 21-year-old at the club after allowing Gonzalo Higuain to leave.
Wenger has remained keen on the youngster since then, and has been buoyed by speculation that Real have altered their stance due to the emergence of Jese Rodriguez.
The Frenchman is desperate to secure adequate cover for Olivier Giroud, who has been the club’s only genuine attacking option for the majority of the season so far.
Lukas Podolski has recently returned from injury, but the German is seen as a wide forward rather than a central attacker by Wenger, while Nicklas Bendtner is not seen as a viable option for a side challenging for league and European honours.
Morata has been used sparingly by Real this term, despite his glowing performance in last summer’s U-21 European Championships – where his four goals secured the Golden Ball award and helped Spain lift the trophy.