The Croatian's agent has been in Milan recently in a bid to facilitate a move, with a big-money swoop to China also on the cards, says The Sun.
But manager Unai Emery could once again find himself hamstrung by a lack of available funds.
The Gunners struggled mightily on the wings last season, with a lack of depth in that area often forcing them into playing sub-par, makeshift wing-backs.
Now Emery wants to add more strength to his wings and sees Perisic as a cheaper alternative to Pepe.
Reports in Italy claim Perisic is very keen on a move to the Premier League - and is more than happy to fulfil that dream at the Emirates.