The Spaniard left Liverpool to join the Serie A side on loan this summer but the shot-stopper's dad claims a deal to move to the Camp Nou had already been agreed
The Spain international was earmarked to replace Victor Valdes, who was heavily linked with a Camp Nou exit after confirming he will not extend his contract with the Spanish champions.
Monaco seemed best-placed to sign Valdes, but the goalkeeper committed to remain with Barca for the final season of his deal.
This also saw Reina's move to Catalunya fall through, as Liverpool sought to sell the 31-year-old following Simon Mignolet's £9 million arrival from Sunderland.
Reina subsequently linked up with former Anfield boss Rafael Benitez on a season-long loan to Napoli, and has become first choice at Stadio San Paolo.
"A few months ago Pepe was in talks with Barcelona," Reina's father Miguel told Marca.
"They had an agreement and he was all set to go but then Victor Valdes didn't leave and the deal fell through."
With Valdes set to leave at the end of the season, Reina reportedly remains a target for Gerardo Martino, with Borussia Monchengladbach's Marc-Andre ter Stegen and Celtic keeper Fraser Forster also noted as possible replacements.
Reina began his career at Camp Nou and made 49 appearances for Barcelona before the emergence of Valdes saw him depart for Villarreal in 2002.