Perisic has been heavily linked with a move away from the San Siro in recent seasons.
However, the Serie A side finally look ready to cash in on the Croatian.
Perisic is valued between €30m (£26.8m) and €35m (£31.3m), according to FCInterNews.
The Italian publication claims West Ham, Leicester and Wolves are debating launching a bid this summer.
However, Arsenal is Perisic’s preferred destination should he leave Italy.
The Gunners are said to have spoken with Nelio Lucas, the winger’s agent, but are unlikely to submit an official transfer bid unless they bring in funds by selling players.
Lucas is in Milan at present meeting with sporting director Piero Ausilio to discuss Perisic’s future.
Arsenal are unlikely to bid £30m for the World Cup runner-up as they continue to search the market for bargain buys.
North London chiefs have ruled out giving Unai Emery a transfer war-chest and have instead told the Spaniard he will only have around £50m to spend unless players are sold.
Arsenal are still battling to sign Yannick Carrasco and Ryan Fraser but both deals are proving difficult.
According to the Evening Standard, Chinese club Dalian Yifang are now undecided on whether or not to sell Carrasco.
The Gunners were hoping that Fraser would take affirmative action to force through a move to Arsenal.
But there are no signs of him doing so yet and Bournemouth are more than happy to keep him, despite the risk of him leaving for free next summer.
Meanwhile, another winger has entered the fray.
Atletico Madrid star Vitolo has reportedly been offered to Arsenal.
The La Liga outfit want Hector Bellerin to move the other way as part of the deal.
Vitolo played under Emery at Sevilla.