The Spain international has been heavily linked with a move to the north London side since the Premier League season came to an end earlier this month.
Morata is thought to be attracting interest from his former employers and Champions League finalists Real Madrid, who have a £24m buyback clause.
According to Daily Mirror, Los Blancos want to re-sign Morata for £24m before selling the striker to Arsenal or Premier League rivals Chelsea and Manchester City at a significant profit.
Morata has won back-to-back Serie A titles since his move to Juventus from Real Madrid in 2014.
The 23-year-old also finished as a Champions League runner-up after Barcelona’s 3-1 victory over Juventus in the final in 2015.
Morata scored seven times in 34 Serie A games for the Italian champions in the 2015/16 season.
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