Reina spent the 2013/14 campaign on loan in Italy after falling out of favour at Anfield.
The arrival of Simon Mignolet pushed him down the pecking order and left the World Cup winner looking for game time elsewhere.
Napoli were delighted to offer him the opportunities he craves, with head coach Rafa Benitez having previously worked with Reina in England.
The 31-year-old has regularly expressed a desire to stay on in Naples, but he is now being forced to accept that uncertainty continues to shroud his future.
A return to Spain has been mooted, with Atletico Madrid said to be keen, but for now it appears as though Reina will be heading back for pre-season training on Merseyside.
His representative, Manuel Garcia Quilon, told Corriere dello Sport: "It's very difficult for Pepe to remain at Napoli.
"From June 30, he will return to Liverpool because they want to maximise his sale, and Napoli are not willing to spend what is required."