It was reported by BBC Sport that the Gunners want to loan the Croatia international with an option to buy him at the end of the season for £35 million ($46m). Meanwhile, Gazzetta dello Sport claims the Serie A side would be willing to let the winger go for a similar fee.
Perisic has long been linked with a move to the Premier League, having been targeted by Manchester United in previous transfer windows. The 29-year-old admitted in December that he came close to joining the Old Trafford side, but was persuaded to stay at San Siro by Spalletti.
The Nerazzurri boss suggested a reasonable offer could tempt them to sell Perisic this time around, but insists Arsenal are yet to put in an offer.
"It is normal that during the market we are talking about a player like Perisic, because he is a strong player that everyone would want in their team," he told reporters when asked about the Croatian's future.
"However, the talk must become concrete and then supported by the correct figures."
Inter are third in Serie A and pushing for a place in next season's Champions League, and Spalletti says he expects Perisic and Real Madrid target Mauro Icardi to keep giving their all to the cause amid ongoing speculation.
He added: "He knows what his job is, so he is expected to continue doing what he knows how to do, even trying to go for more like all the players, as well as Mauro Icardi. Mauro is having a season in line with his value."
Perisic has made 25 appearances in all competitions for Inter this season, scoring three times. His current contract runs until 2022.