The Gunners have made a move for Inter Milan winger Perisic with a loan with an option to buy.
BBC Sport journalist David Ornstein revealed the interest on Twitter.
“Arsenal have made an approach to sign Inter Milan winger Ivan Perisic,” he tweeted.
“#AFC want loan with £35m option to buy. 29yo open to #Inter exit.
“Fits plan of versatile midfielder e.g. Suarez (still possible) / Nkunku + winger. Unclear if injuries mean defender wanted but Sokratis not bad.”
Mesut Ozil has been attracting attention from the San Siro outfit in recent weeks but it is not specified whether any deal would see the German go the other way.
United have long held an interest in Perisic, with Jose Mourinho desperate to bring the Croatian in.
Perisic confirmed the Old Trafford outfit’s interest in him by saying: “It’s true that an offer from Manchester United was on the table and I was close to leaving Inter.
“But I decided to stay and, as I said, Luciano Spalletti’s perseverance to keep me played a big role. In football, small details in these situations are key.
“Admiration from a coach like Jose Mourinho is definitely something that flattered me.
“It’s confirmation of hard work and good performances.”
However, the Red Devils would not adhere to Inter’s £45m price-tag and The Special One was left wanting.
The Portuguese coach has since been sacked but Ole Gunnar Solskjaer is also interested in signing the 29-year-old, according to Sportmediaset.
United are not expected to make any signings this month but the outlook could change in the coming days if a situation presents itself.
Arsenal are desperate to sign two players, a centre-back and a winger, but with no funds only loan deals can be struck.