Kagawa joined the Red Devils from Borussia Dortmund in the summer of 2012, but has struggled to make a huge impact in English football.
The 25-year-old made 20 Premier League starts for United during their championship-winning campaign of 2012/13, and has started just 13 league fixtures this term.
With United set to appoint a new manager in the summer, there have been suggestions that Kagawa might be on his way out of Old Trafford.
Serie A outfit Napoli have been linked with a move for the former Cerezo Osaka star, but the player's agent has insisted that coach Rafael Benitez has no made no contact with him.
"Has Benitez made contact with Kagawa? These are just rumours," Thomas Kroth told Ultimecalcionapoli.it.
"He is not unhappy at Manchester United, so there's no reason to talk about him departing to another club."