Darmian played against Liverpool in the International Champions Cup despite the uncertainty over his future.
The 28-year-old, who has struggled to cement a starting place since joining from Torino in 2015, then confirmed his intention to seek a new club.
Darmian played just 8 EPL games last season, providing back-up to Manchester United's regular full-backs, Ashley Young and Valencia.
The Italian is one of several Red Devils first-team players free to leave and had been strongly linked to Juventus earlier in the window with Inter Milan another club rumoured to be keen.
When asked if Serie A would be his preferred destination, he said: "It's an option".
De Laurentiis though has spiced up the conversation by confirming his interest in signing Matteo, potentially speeding up any negotiations.
But he added that Napoli also have alternatives lined up: "We are looking at six profiles". There could also be Benjamin Henrichs from Bayer Leverkusen. "I want to leave but we will see what happens because we don't know".
Napoli have now turned their attention towards Darmian and are expected to approach Manchester United for a loan deal.
"But yes, I still want to leave, that what I want".
"I hope that the boys on deserved holidays take care of themselves a bit and that somebody wants to do what Rashford and Phil Jones made a decision to do, which is to be back a bit earlier to try to help the team because for the beginning of the season we are going to be in trouble", Mourinho told reporters on Sunday.
Martial revealed the news on Instagram with an image of the boy's feet with the caption: "Thank you Lord for giving me a second attractive child in good health". It is a hard decision to leave.