Following reports the Dortmund playmaker had flown to England, representative Thomas Kroth affirmed that his client held talks with the United boss
The 23-year-old is expected to leave the Bundesliga and DFB-Pokal winners this summer, with Dortmund sporting director Michael Zorc having revealed that his client has turned down a contract extension past his current deal, which expires in 2013.
And after reports emerged on Tuesday that the player had flown to Manchester, agent Thomas Kroth confirmed to Goal.com that talks took place with Ferguson early in the day.
Both Manchester United and Kagawa are interested in a transfer, Kroth told Kicker, but the representative revealed that "The outcome is open."
Thus far no other clubs have been closely linked with Kagawa, who is reported to be angling for an attractive offer from an English club.
Zorc, meanwhile, has confirmed that he is willing to listen to offers for the playmaker, with Dortmund reported to be holding out for a €15 million bid.
Speculation linking Kagawa with a move to Old Trafford has been rife in recent weeks, with Ferguson having observed the Japan international during Saturday's DFB-Pokal final victory over Bayer Munich in Berlin.
Kagawa was a key figure in Dortmund's title-winning season, scoring 17 goals and giving 13 assists in 42 matches in all competitions.