The Colombia international is expected to leave Real this summer after a battling season in Madrid. James had spent the previous two seasons on-loan with Bayern Munich, but upon his return has struggled to win over coach Zinedine Zidane.
Tuttosport says Juventus are monitoring developments, but City are also watching the situation.
It's suggested should Kevin de Bruyne push to leave this summer, City will move for James as a replacement for the Belgium international. As such, City's interest raises the prospect of a swap deal.