Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The Japan international has been a largely peripheral figure since joining United last summer from Borussia Dortmund, both under Sir Alex Ferguson and his successor David Moyes.
Kagawa was substituted at half time during Saturday's 2-1 loss to West Brom and he acknowledges that he needs to make a greater impact if he is to remain with the Barclays Premier League champions.
He said: "I have to take this like some kind of message (from the manager).
"I need to improve more and more, or I cannot survive at this club.
"I have to take this in a positive way and keep trying to do my best."
The West Brom clash was Kagawa's first league start of the season, although he did star in the Champions League win over Bayer Leverkusen, and he feels he could have been of use if he had stayed on against the Baggies.
"I thought that I would have been able to find some space to create the chances in the second half," he added.
"In that sense I was disappointed. Sure, I wasn't involved that much. I didn't touch the ball enough but I was trying to be patient so I didn't feel that bad."