Osimhen managed 10 goals in 30 appearances across all competitions in his first season at the club.
Last season, the Nigerian international scored 18 goals and provided six assists in 32 appearances across all competitions for the Partenopei.
That 23-year-old also spent over two months on the sidelines after picking up an injury in a league match against Inter Milan.
Osimhen reported for pre-season training with the rest of the Napoli squad in Dimaro on Wednesday.
Spalletti was delighted to welcome back his star striker and hopes he gets better ahead of the new campaign.
“He is a fantastic player who can become extraordinary because he has so many things to learn,” Spalletti said at a press conference in Dimaro.
“Having him available from the start and more time on the pitch, it will be easier to catch those things where he needs to improve.”