Osimhen was one of the revelations of the recently concluded Ligue 1 season.
Club owner Aurelio De Laurentiis is looking to retool his squad after missing out on next season's Champions League. Despite an uptick in form under manager Gennaro Gattuso, the Partenopei can finish no higher than fifth in the Serie A table.
Osimhen joined Lille last summer from Belgian side RSC Charleroi for a reported €14 million and scored 13 goals in Ligue 1 before the season was abandoned. The 21-year-old's performances drew admiring glances from some of Europe's top clubs, including Manchester United and Chelsea, but Napoli apparently moved the quickest.
Napoli have also been linked with Osimhen's teammate, defender Gabriel Magalhaes, but it remains to be seen if they'll meet his €30-million price tag.
Osimhen would replace Arkadiusz Milik in Napoli's front line. Gattuso confirmed earlier in July that Milik asked for a "change of scenery." Juventus are reportedly interested in signing the Polish striker, who's scored 14 goals across all competitions this season.
Boga could join Osimhen at the San Paolo if negotiations are successful. Known for his dribbling skills and unpredictability, the 23-year-old has become a hot commodity in Serie A. Sassuolo paid just €4 million to sign Boga from Chelsea in July 2018.