The Celtic centre-back, who arrived at Parkhead from Groningen in the summer, is happy to stay with the Scottish Premiership club but admitted "anything is possible"
Van Dijk only moved to the Scottish Premiership side in June 2013 from Groningen and is understood to have attracted interest from England's current top two clubs.
The 22-year-old has welcomed links with the Premier League pair, but is happy to stay with the SPFL side having settled in well in Scotland.
"It's fantastic when you're linked to absolutely top clubs," Van Dijk told Voetbal Internatonal.
"It's a cliche, but in football everything is possible. I know very good what I have here at Celtic and I'm still glad to be here."
Manchester City have been in the market for a defender and have previously sent scouts to watch Porto pair Nicolas Otamendi and Eliaquim Mangala, Goal understands.
The Etihad Stadium side will not allow Joleon Lescott to complete a move to West Ham in January until they have signed a replacement.