HITC Sport understands that the Japanese defender is on his way to the King Power Stadium.
The 28-year-old has been with Inter since 2011 and has played over 150 games for the Italian giants, covering a number of positions.
Nagatomo is a full-back able to play on either side of the defensive line and Leicester boss Claudio Ranieri has made the move to tie up a deal with Inter.
HITC Sport understands that Leicester have agreed to pay £3million for Nagatomo, who is now due to undergo a medical in England.
Nagatomo would become the second Japanese star to make the move to Leicester this summer, following striker Shinji Okazaki to the club.
The Foxes have made a bright start to their 2015/16 Premier League campaign, collecting seven points from a possible nine, and will be hoping to continue that run today away at Bournemouth before turning their attention to the final few days of the transfer window.