Inter have reportedly rejected a loan offer made for the 29-year-old by the Gunners, whose boss Unai Emery has already confirmed he will only be able to sign players on a temporary basis in January.
But a potential move for Perisic may have edged closer, with Luciano Spalletti having left the Croatia international out of his starting XI for Sunday's 1-0 defeat at Torino
Perisic starred at Russia 2018 as Croatia made it to their first World Cup final, but his form for Inter has tailed off, with the former Wolfsburg star having netted just three goals across 25 appearances in all competitions so far this campaign.
Spalletti hinted in his pre-match news conference that a deal could be done, but Inter's head coach told Sky Italia that the price must be right.
"It's a player that has been talked about because everyone values him as much as we do, and if anyone wants to buy him they will need to pay him good money because we rate him a lot," he said.
It nows seems that deal for the winger is even closer after Marotta told Sky Italia that Perisic has requested to leave the club.
"Perisic has asked to be sold and we have to try to satisfy him by respecting the value of assets," he said.
"No concrete offers have arrived yet but we have to understand and meet him. If he stays with us we will try to give him the chance to get to the end of the year."
Following the match, Spalletti suggested that he could be frozen out at San Siro no matter what happens in the rest of the window.
"Players can say what they want, but they are owned by clubs and to give them away needs someone to buy them," the coach said to Sky.
"If he does not want to play, he will stay out. There are no problems. When you think you can't make a help, you can do it staying out".
It therefore it seems likely that should Arsenal sign Perisic it would have to be on a permanent deal, something which could scupper any proposed move.
The Gunners have also been linked with loans for Barcelona’s Denis Suarez and Paris Saint-Germain’s Christopher Nkunku.
Should any of the above sign for Arsenal they will join an injury-ravaged squad.
Unai Emery is without key defenders Laurent Koscielny, Sokratis Papastathopoulos and Hector Bellerin, and it has therefore also been reported he may attempt to bring in some defensive cover before the window closes on Thursday.