The Reds boss has admitted the club's decision to offload the keeper because it cannot justify his 127,000 euro-a-week wages following the arrival of Simon Mignolet.
Goal reported this week that the Serie A side had turned its attention to the Spain international after growing impatient at Julio Cesar's reluctance to accept a contract offer, and Rodgers has now confirmed that Reina will leave Liverpool this summer.
"Financially it is something we needed to look at," Rodgers told the Liverpool Echo. "That would be the reason because obviously you wouldn’t move on a top goalkeeper. It reared its head over the last few months and I had to prepare for it by bringing in a new goalkeeper.
"Pepe is a good guy. I’ve a lot of time for him, and he understands what I want to do totally. He’s got a big season ahead because it’s a World Cup year and one where, if he wasn’t going to be playing, could severely harm his chances of going."
Reina, who has three years remaining on his contract at Anfield, will be reunited with former Reds boss Rafa Benitez at Napoli.
The Spanish coach has already signed young goalkeeper Rafael from Santos for 5 million euros earlier in July, but wants a battle-hardened No.1 for the new campaign, and one who can also guide the 22-year-old Brazilian.