Clarets face competition for Nagatomo
The 30-year-old moved to the San Siro in 2011 from newly-promoted Cesena for â‚¬10.95m following a successful season on loan in Serie A.
He has gone on to make 185 appearances in all competitions for Inter, and has previously been linked with a move to Manchester United.
Sources close to Inter claim Nagatomo has offers from Burnley and Sunderland, and Inter are prepared to do business.
Reports in Italy suggest a fee of between â‚¬6-7m would be enough to secure his services, but the player himself is believed to be happy in Italy, however, and last year reportedly refused an offer from United.
Nagamtomo is also engaged to Japanese actress Airi Taira, and is due to get married in the coming months, which could also affect any decision.