This report comes after the Italian club's general director vowed on Thursday to "try [everything] they can" to secure the 24-year-old's signature.
Speculation has been mounting in this transfer window about the future of the Liverpool midfielder as it appears increasingly unlikely that he will sign a contract extension with the Merseyside club.
Serie A champions Juventus have been leading the race with early reports in January suggesting that the German international had signed an agreement to arrive in Turin at the end of the season.
However, this doesn't seem to be the case as the Premier League leaders hope to hijack their move for the player.
Considering the City's limited scope to sign established stars due to Financial Fair Play, the possibility of waiting to sign Can on a free transfer in the summer appears to be too tempting to Guardiola.
The midfielder has made 107 appearances for Liverpool since joining from Bayer Leverkusen in 2014, scoring eight goals,