Szczesny is expected to leave the Emirates Stadium on a permanent deal this summer following his time on loan at Roma, where he impressed across the past two seasons.
Juventus have already been tipped to make an approach, seeing the Pole as a potential replacement for Gianluigi Buffon, but reports earlier this week suggested that Arsenal are refusing to sell for anything less than £20m.
Recently-appointed Inter boss Spalletti sent out mixed messages when asked about his interest in Szczesny, while also admitting that Fiorentina midfielder Borja Valero is also out of his reach due to Financial Fair Play regulations.
"Borja is a player we had already tracked at Roma and who Inter were observing before my arrival," he told Sky Sport Italia. "I know that he will change club this summer, but for the moment we are sorted in that area. In any case, he is certainly a player you can rely on.
"Are you trying to make me argue with all my current players? We already have Samir Handanovic, who is very experienced and strong. I've already worked with him and I know his quality. For the moment we've got him. Then obviously Szczesny is a modern player, because he can use his feet and in modern football you need that to start moves from the back.
"We want to do something important this season and we have strong players in the squad, so first of all we'll take into consideration those we've got and who I like. Then, looking at Financial Fair Play, we'll try to improve the squad, focusing on sales first.
"It might seem as if Juventus, Roma and Napoli are impossible to catch, as it won't be easy to get an extra nine or 10 victories per year. Our objective is to give Inter back the history it deserves."
Szczesny, who made 35 Serie A appearances for Roma last season, has been on Arsenal's books since 2006.