The Independent says City are actively discussing a move for the former Manchester United and Juventus midfielder.
After seeing his four-year doping ban cut to 18 months on appeal, Pogba can play again in March.
The France international is available after having his contract with Juve terminated by mutual consent last month.
City are now exploring the prospect of bringing Pogba back to Manchester, though for the moment, he is reluctant to consider the move given his United background.
