The attacker has been linked with Manchester United and he's welcomed the interest.
But Kagawa's agent, Thomas Kroth, says the player is likely to commit to Dortmund after opening negotiations with the club to extend his deal.
"We have even had a first round of talks with Dortmund general manager Michael Zorc with regard to a new contract."
He added: "Shinji is actually contracted to Borussia Dortmund and he likes the club. He is absolutely looking forward to playing in front of the exciting Signal Iduna Park crowd in the Bundesliga and the UEFA Champions League in the new season."