The 33-year-old has been in excellent form for Los Blancos this season, scoring 15 times and contributing eight assists in 17 appearances in all competitions.
The France international's current deal at the Bernabeu is due to expire in June 2023, though, and Carlo Ancelotti's side are thought to be targeting moves for both Paris Saint-Germain's Kylian Mbappe and Borussia Dortmund's Erling Braut Haaland.
Man City failed to sign Harry Kane from Tottenham Hotspur over the summer despite a host of speculation and therefore remain in the market for a new striker.
According to El Nacional, the Premier League champions have contacted Benzema's agents to discuss the possibility of a switch to the Premier League, and the Frenchman's camp have been 'very receptive' to the idea of moving to the Etihad Stadium.
The four-time Champions League winner has scored 294 goals and registered 152 assists in 576 appearances for Real Madrid since arriving from Lyon in 2009. body check tags ::