The 38-year-old has hinted he would be interested in a return to Serie A when his contract with LA Galaxy expires at the end of the MLS playoffs.
Ibrahimovic has said before he would like to play for Napoli before retirement, having previously won Serie A with Juventus, AC Milan and Inter, although his two titles with the Old Lady were revoked following the calciopoli scandal.
Napoli boss Carlo Ancelotti, who worked with Ibrahimovic at Paris Saint-Germain, has already said the club are "waiting" for the Swedish star to arrive.
De Laurentiis, who met with Ibrahimovic in Los Angeles by chance, has suggested the player need only agree to a Napoli offer and the deal can be concluded.
"[Ibrahimovic] is a friend," he told Sky Sport Italia. "I met him in Los Angeles not as a footballer but as a normal person because we were in the same hotel.
"I invited him over for dinner with his wife and kids and we had an amazing time. It would be my wish to see him in Napoli colours. It's more than a suggestion and it depends on him. It's been talked about for a few months now."
Ibrahimovic has scored 30 goals in as many games in MLS in 2019, helping Galaxy reach the playoffs.
Having beaten Minnesota United 2-1, Galaxy will now meet city rivals Los Angeles FC in the Western Conference semi-finals on October 25.