The Uruguayan hit-man – who netted a stunning four-goal haul against Norwich earlier this week – was heavily linked with a switch to Los Blancos over the summer, after actively seeking a move away from Merseyside.
However the Reds stood firm to keep their man, even when faced with a £40m offer from Arsenal.
Rumours have suggested that Real’s interest has since cooled, with some reports claiming that Sergio Aguero is now their preferred target to create a fearsome attacking threesome with Gareth Bale and Cristiano Ronaldo – the two most expensive players on the planet.
But following Suarez’s 13 goals in nine league outings this season, the Madrid giants are now swaying back towards the Kop icon.
It is believed that members of Real’s hierarchy are sure that the 26-year-old is ready to swap England for Spain, and that they are also convinced that negotiating with Liverpool will be far easier than thrashing out a deal for Aguero with City.
A January move appears unlikely with Suarez having suggested that he is ready to stay, but a switch next summer may be on the cards if Brendan Rodgers is unable to guide his side into the Champions League.