Nagamoto claims United boss Louis Van Gaal wanted him to move to Old Trafford.
But Nagamoto insists that he is happy at San Siro and is ready to sign a new deal with the club.
“I like everything about Inter, I want to stay here and renew my contract,” Nagatomo told Inter’s TV channel.
“I turned down an offer from Manchester United, as my desire is to stay here. I have an excellent rapport with Roberto Mancini.”
He added: “I love Italy. I’ve been here for five years now and I feel at home.”
“Hopefully, when I finish my career, I can stay in Italy.
“This season is my best spell at Inter. We have a great group here and I get on well with everyone.”