Borussia Dortmund have expressed interest in re-signing the Japan international this week.
But Moyes was keen to stress that United weren't considering giving up on Kagawa after the Japanese international failed to meet expectations in his first year at Old Trafford.
Moyes said: "It was his first season in the Premier League last year. He's a young player so we hope his development continues. I look forward to working with him and hopefully he has a really good season coming up."