"Right now, it's just about me being successful here with Dortmund," Kagawa told German newspaper Die Welt on Sunday having been linked to both European teams in the German and Japanese media in recent months.
"There are rumours (about Manchester United or AC Milan) again and again, but I have no information about that. The talk leaves me cold."
The 22-year-old joined Dortmund in 2010 from Japan side Cerezo Osaka for just 350,000 euros, but after helping Dortmund win the German title last season, his market value has soared to around 14 million euros.
He has a contract at Dortmund until 2013 and is back in form after missing the first few months of 2011 after breaking his foot while playing for Japan at the Asian Cup last January.
"For a player like me to come here and win the championship is really an honour," he said.
"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 do so in the future."