The Japan international hopes to use his country's disappointing exit from the World Cup as motivation as he fights to earn a place in the Red Devils first team
Kagawa joined the Red Devils from Borussia Dortmund in the summer of 2012 but struggled to nail down a regular place in the line-up under former managers Sir Alex Ferguson and David Moyes.
Following the big-money arrivals of Juan Mata in January and Ander Herrera in June, the Japan international has been linked with a move back to Dortmund this summer, potentially as a makeweight in any deal for Mats Hummels.
But he has hinted to AFP that he could stay at Old Trafford and fight for his place under Van Gaal: "I feel incredibly excited.
"It’s a new start and I feel re-energised. It’s up to the players to get the results we need. I have a strong desire to do well.
"I’ll look more closely at my game and accept the challenge filled with passion."
Kagawa was part of the Japan squad which finished bottom of their World Cup group in Brazil this summer, but he has vowed to use that failure as motivation in the coming months.
"It was the most disappointing experience of my life. How I can use that as a plus will depend on how hard I work."