The German is in talks about joining the Premier League side after the European Championships.
The Star claims that the Sky Blues have earmarked the Real Madrid midfielder as one of their main targets for the summer, and are now closing in on a £37.5m deal to bring him to the Etihad.
Pep Guardiola reportedly wants the 26-year-old to form a partnership with international teammate Ilkay Gundogan - who has already completed his move to the Premier League - in the centre of City's midfield, the Star reports.
If City manage to pull off a deal for the former Bayern Munich star, he would undoubtedly be one of the biggest names to arrive in England this summer.
Kroos has already won a tremendous amount of major honours throughout his career, including two Champions League medals and of course, the World Cup in 2014.
And he has shown during the ongoing European Championships that he is still determined to lead his side to success. He has arguably been Germany's best player at the tournament so far, and Guardiola will be hoping that if he can get a deal across the line, he can replicate that form in England next season.