According to Italian newspaper Tuttosport, the Gunners have made an approach for the Juventus striker, who is also a reported target of Premier League rivals Liverpool.
The Reds have already made a formal approach for the player, and have reportedly made a £45m bid for the Italy international, which has been rejected immediately.
Morata impressed for the Bianconeri in the 2014-15 season, but has fallen down the pecking order in Turin.
He proved himself to be a big game player for Juventus after scoring few important goals last season, but so far has only managed one Serie A goal to his name.