TalkSport reports that Liverpool boss Kenny Dalglish is keen to strengthen his squad in the January transfer window and has sent scouts to watch Kagawa in action.
The 22-year-old is rated as one of the best young midfielders in Europe.
Kagawa’s current contract with Borussia Dortmund is set to expire in the summer of 2013 and it is not expected that the Bundesliga side will let the Japanese international leave for less than £18million.