Two years ago, the Uruguay international signed a contract extension to remain with the Partenopei until 2015, but on Wednesday in Milan he revealed a move north was imminent.
Quoted on Tuttosport, the 28-year-old told Sky: "I'm moving to a great club. Inter have wanted me for a while and so I will do my best to repay the club."
If the anticipated loan deal goes through, at an estimated cost of 1.25million euros, Gargano will line up behind Italy forward Antonio Cassano, who completed his transfer from AC Milan on Wednesday morning.
The Uruguayan continued: "The competition for places is a beautiful thing.
"Everyone has to play their best at all times. Cassano is a champion and a great personality."
Gargano made over 163 appearances for Napoli since joining from Danubio in 2007.
He added: "I will be Neapolitan for the rest of my life. Two of my children were born there and the city will always be in my heart.
"I'm sorry, it was great playing for Napoli but this is a new adventure for me."
Napoli captain Paolo Cannavaro wished his team-mate well in Lombardia.
He told Tuttosport: "We've brought in a lot of new players and for him it was the best choice, he's been honest and sincere about that."
"You have to love Napoli to play here. If someone doesn't think this is the perfect place, it's right that they take a different path.
"Only he who stays knows how much this shirt means."