The North-West outfit are expected to complete the signing of Mata from Chelsea within the next few days, which could place Kagawa's role within the team in danger.
The 24-year-old has failed to secure a regular first-team spot under manager David Moyes this season, which has sparked rumours that the Japan international could return to Borussia Dortmund or join Atletico Madrid.
However, Kroth told Sky Sports News: "At this moment I am sure Shinji will stay. There has been no contact and so it is just rumours."
When asked if Mata's arrival will affect Kagawa's fate at the club, Kroth said: "No, it is my opinion that he will stay."
Kagawa was signed by former manager Sir Alex Ferguson in 2012.