Nagatomo, 33, is currently a free agent after his Galatasaray contract expired on June 30.
After two and a half successful years in Istanbul, winning four trophies, the veteran is now looking for another club.
And any offers arriving from Italy would be given priority by Nagatomo.
The first club to show interest in Nagatomo is newly-promoted Benevento, who are signing high profile veterans.
Their interest in Nagatomo has not yet led to an offer being made, but that could change in the near future.
Nagatomo has already turned down three proposals, one from Turkey and two from the Middle East.
He said no to a one-year contract offer worth €500,000 from Besiktas out of respect to Galatasaray, a club he grew to love.
And he also turned down an approach from Saudi powerhouse Al-Nassr as a move to the Middle East is not his priority.
Al-Nassr head coach Rui Vitoria had wanted Nagatomo to play as a left winger instead of left-back.
An unnamed club from the United Arab Emirates also sent feelers, but also had no luck.
Dreaming of Italy
The Samurai Blue star is waiting to see if any concrete offers come from Italy before considering other leagues.
He was a mainstay in the Inter side for seven and a half seasons before moving to Galatasaray.
In 2016, he proposed to Japanese actress Airi Taira on the San Siro pitch and they married the following January.
At the age of 33, Nagatomo is still in good physical shape and believes he has plenty to offer.
Several J.League clubs would no doubt like to take him back to Japan, where he played for FC Tokyo in the past, but that may be a couple of years away.
Nagatomo has made a remarkable 122 appearances internationally for Japan since his debut in 2008.