The Japan international winger has been tracked by the Premier League champions for some time, with AC Milan also thought to be interested, but the 22-year-old is not focussing on the speculation.
“Right now, it’s just about me being successful here with Dortmund,” the attacker old German newspaper Die Welt.
“There are rumours about Manchester United and AC Milan again and again, but I have no information about that. The talk leaves me cold.
“For a player like me to come here and win the championship is really an honour. I have really experienced a lot. I soon found my place in the team and we were successful.
“Winning the championship at the end of the season was great. I must admit it was beyond my wildest dreams.
“In my time here, I’ve seen that Borussia Dortmund has developed steadily. We have become German champions and played in the Champions League.
“In the Bundesliga, we are up at the top and want to maintain this in the future,” he concluded.
Jurgen Klopp’s side paid less than £300,000 for Kagawa back in 2010, but any potential suitor would need to chalk up at least £10 million to even interest Dortmund.
By Gareth McKnight