The goalkeeper is currently on loan from Liverpool, who are flying high in the Premier League, and the third-placed Serie A side hope to sign him permanently
The 31-year-old is on a season-long loan from Liverpool, who are currently top of the Premier League, and has largely been a hit during his time at the Stadio San Paolo under Rafa Benitez.
Following the Partenopei's impressive 2-0 win over Juventus on Sunday, which offered hope that the victors could yet catch Roma in second place, whom they are six points behind having played a game more, club chief De Laurentiis revealed the Spaniard could make his move to Naples permanent.
"I talked to Reina," he wrote on his Twitter account. "If they finish in second place I'll reward them all, but I also want him to stay.
"Winning against Juventus is always special, we don't hate them but we support Napoli passionately, that's all."
The goalkeeper, who has yet to confirm his intentions once the season finishes, heralded the win over the Scudetto holders in which he successively kept a clean sheet.
"What an important victory as we continue to look for the second place!" Reina tweeted.
Napoli are back in action on Sunday when they travel to Parma, who have suffered back-to-back defeats against Juve then Lazio.