Manuel Pellegrini has recently reinstated Joe Hart as his number one after a shaky opening to the season saw the England international dropped in favour of Costel Pantilimon, but the ex-Malaga coach is still rumoured to be unconvinced by his stopper.
The Chilean is a fan of Lopez – who has established himself as Real’s number one ahead of club icon Iker Casillas – and has been impressed by his composed and authoritative displays at the Bernabeu.
The 32-year-old is also wanted by Borussia Dortmund, but if the Germans make any move City are likely to rival their pursuit before the month ends.
Pantilimon is said to be close to leaving the Etihad Stadium later this year, which could leave Pellegrini short of options.
Lopez would be in direct competition with Hart if the move materialises, which the Sky Blues chief hopes will bring out the best in both players and provide him with at least one world class glovesman.
City could also move for Casillas, who could be available this month after expressing signs of distress at a lack of playing time in the build up to the World Cup.