The Spanish goalkeeper moved to Italy in 2013 on a season-long loan deal from Liverpool.
And with his parent club having deemed him surplus to requirements, there would appear to be little future for the World Cup winner at Anfield.
Reina has announced that he will consider all of his options at the end of the current campaign, with several sides believed to be considering an approach for his services.
Napoli, though, hope that they can persuade the 31-year-old to remain in Serie A and help them to build on a productive campaign which could see them snatch second place.
De Laurentiis told a press conference in the wake of Sunday's 2-0 victory over table-topping Juventus: "After yesterday's victory I went down to the locker room and I promised the players a bonus if they can finish second.
"Then I talked to Reina and told him that he must remain with us. I want him confirmed for next season.
"He was happy, for him it was a double reward."