While Nagatomo is currently with Inter for their pre-season tour of China, there is growing speculation that he will leave the San Siro after five seasons after struggling for playing time.
Last month, La Gazzetta dello Sport reported that West Brom, Schalke 04 and Sampdoria were all interested in signing the Japan international.
Italian publication TMW claim that Stoke City are now in the mix of teams that are hoping to acquire the services of the 28-year-old full-back.
Nagatomo, whose contract with Inter expires in June 2016, has already represented his country 81 times, including at the 2010 and 2014 World Cup.
The 28-year-old has been playing in Italy ever since he joined Cesena from FC Tokyo in July 2010. He then went on to sign with Inter in January 2011.