The Dutch defender only made the move to Parkhead in the summer but his future is already being speculated on following his impressive start to life in Scotland.
City are believed to be one of a number of clubs monitoring the progress of the 22-year-old as manager Manuel Pellegrini considers reshuffling his defensive options in the summer.
With Joleon Lescott set to leave at the end of the season when his contract expires, Pellegrini might be tempted to move for Van Dijk if he continues to impress north of the border.
However, City aren't the only club monitoring Van Dijk's progress as Chelsea and Arsenal have been credited with an interest.
The former FC Groningen youngster says he is happy to be linked with a move to the Premier League and has rubbished the suggestion he has already held talks about a move to England.
Van Dijk told Dutch football magazine Voetbal International: "It's fantastic that such top teams are being linked to you.
"I haven't spoken with anyone yet, but it's always a good sign, but I am enjoying it here at Celtic. The first six months were fantastic."
When asked whether he could decide to leave this month, Van Dijk said: "It's a cliche, but in football everything is possible.
"What I know is that I am in a good place here at Celtic and that feels excellent."