The Juventus striker prefers a move to Chelsea or Manchester United.
The forward looks set to return to Real Madrid in the coming months as the La Liga club appears keen to activate a release clause they put in the deal that first took him to Serie A.
Morata looks unlikely to stay at the Bernabeu long term though, with the Champions League holders reportedly eyeing a quick sale and an easy profit for the Spaniard.
Arsenal have been heavily linked for a while now, with Corriere dello Sport claiming last month that they had made a huge £51million bid to secure him ahead of the competition this summer.
So far a deal has not been completed and it appears that if the Gunners are seriously interested then they will be left disappointed.
According to the latest report from AS, Morata knows he will be second fiddle to Karim Benzema and will look to move, but he is not interested in making the Emirates Stadium his next home.
Instead he wants a move to either Chelsea or Manchester United where two of his former managers, Jose Mourinho and Antonio Conte, will be in charge next season.
That will come as a blow to Gunners boss Arsene Wenger, who is still waiting for a decision from Jamie Vardy and another target may now need to be identified.