The former Borussia Dortmund playmaker has struggled to establish himself at Old Trafford since his £12m move in summer 2012.
He has made just 24 Premier League starts but earned praise for his second-half display against Swansea in the Premier League last weekend, when he was moved into his favoured central position.
Kagawa told United's official website: "I think I can still improve my strength. I'm not the tallest or biggest player, so I have to move my body more.
"Smaller players in the Premier League are very good at using their bodies (to get past the opposition) and that's what I will continue to do.
"I realise the Premier League is a very tough league and I know I have to be stronger."