The Mirror says Real Madrid are demanding around £15million, and a potential buy-back clause after two years, for the Spain Under-21 striker.
The Gunners tried to sign Morata in January, but Real blocked it after boss Carlo Ancelotti insisted they would not let him go.
But Morata is now open to a move and Real accept they cannot guarantee him more games which leaves Arsenal in pole position.
Arsenal are looking for at least two forwards with Nicklas Bendtner set to leave this summer and they remain keen and hopeful on Schalke's emerging talent Julian Draxler who was their No1 target in January.
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