The French forward is currently Los Blancos’ main striker, but with his contract due to expire at the end of next season his future is in doubt.
Real are believed to be keen to thrash out a fresh deal with their man, but an agreement is said to be some way off.
This has alerted Chelsea and City, with both clubs ready to offer him a Premier League-shaped escape route.
Blues boss Jose Mourinho is perhaps the more interested of the two managers involved, with the Portuguese coach known to be desperate to add a world-class goal-getter to his ranks.
The current Stamford Bridge chief is understood to be a fan of Benzema after working with him in Spain, and could push to set up a reunion.
But City are also in the hunt as they themselves look to bolster their options.
With Edin Dzeko looking likely to leave at the end of the current campaign, Manuel Pellegrini is ready to add to his ranks, and partnering Benzema with Sergio Aguero is seen as a tempting option.
The Real man is likely to command a fee in the region of £40m.