The Spain international was reunited with Rafael Benitez, the manager who took him to Anfield in 2005, when he agreed a season-long switch to Stadio San Paolo in July.
Reina's career at the Merseyside club looks to be over, with Simon Mignolet now established as first-choice keeper under Brendan Rodgers, and De Laurentiis is eager to bring the 31-year-old back to Naples in the close-season.
The Napoli president has also revealed that Benitez's squad will receive a bonus if they can secure second place in Serie A.
"I spoke with him (Reina)," said De Laurentiis.
"I made him a promise that in addition to the premium for second place, I want him confirmed with us."
Reina kept a clean sheet in Napoli's 2-0 victory over Serie A leaders Juventus on Sunday - a win that puts them six points adrift of second-place Roma.
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