After coach Jose Mourinho revealed the defender wants to leave United, Darmian confirmed he wants a fresh start and more regular playing time.
A return to Italy has been mooted, with Juventus and Inter named as potential destinations alongside Napoli, and Darmian said in February that he would be open to offers from any of the three Serie A sides.
De Laurentiis is hoping it is last season's runners-up who can lure him back to his homeland as they look to challenge for the title once again.
"It's true that we asked for Darmian on loan with a right to buy," he told Radio Kiss Kiss Napoli.
Since joining from Torino in 2015, Darmian has made 85 appearances for the Red Devils, but featured just eight times in the Premier League for Jose Mourinho's team last term.
However, the Italy international is not Napoli's only option to strengthen at full-back, as the film producer admitted Benjamin Henrichs and PSV right-back Santiago Arias are possibilities too.
"We are looking at six profiles," he added. "There could also be Benjamin Henrichs from Bayer Leverkusen.
"Regarding Santiago Arias, I don't know yet, we are on the way, so it's all to see."
The Partenopei chief also admitted that reported interest in Mexico and Standard Liege goalkeeper Guillermo Ochoa is true, but would not go into detail.