City were understood to be interested in the Dutch international during the summer, but Van Dijk instead decided that he wanted to join Liverpool.
No deal materialised for Liverpool, though, and The Mirror reports that the Reds will again face opposition for his signature in January after City boss Pep Guardiola confirmed that he would target defensive reinforcements.
Only Manchester United have conceded fewer goals than City this season, although the Premier League leaders will have to cope without John Stones for up to six weeks after he sustained a hamstring injury.
"We're going to discuss when January is coming. We are going to think about it, but not because John is in that position," Guardiola told reporters.
"To play in all the competitions, you need a bigger squad because the players don't have time for regeneration before the next game."
Van Dijk has made seven appearances for Southampton so far this season, having missed the start of the campaign through injury.