The 23-year-old has been offered a new contract by the German champions but he is seemingly set on a move to England, with Manchester United said to be particularly keenBorussia Dortmund boss Jurgen Klopp has resigned himself to losing Shinji Kagawa to the Premier League, claiming that in the attacking midfielder's native Japan, the Bundesliga "means nothing".
Kagawa still has a year to run on his current deal with the reigning German champions but has rejected the offer of a new contract.
Klopp has given up hope of the 23-year-old changing his mind, believing that Dortmund simply cannot compete with the lure of the Premier League.
"We cannot take away Shinji's childhood and his Japanese culture," the 44-year-old coach told Suddeutsche Zeitung.
"Where Shinji was born, our league means nothing, there is only the English Premier League.
"But it is certain that Shinji had to do something incredibly difficult, to make a decision against us.
"Anyone who leaves us carries the greatest doubt as to whether he makes the right decision."
Kagawa, who arrived at Signal Iduna Park from Cerezo Osaka in 2010, is believed to be one of Manchester United's principal summer transfer targets.