AS says Abramovich is ready to sanction a 35m swoop for the Spanish full-back this summer.
Even if Real are willing to do business, the Russian billionaire may have difficulty persuading Ramos to leave Madrid, after he said he's love to stay at the Bernabeu "for life".
He told Fifa.com: "As for the future, you can never say what's going to happen in football, although I am happy here. I'm very grateful to Sevilla and Madrid for having moulded me as a player and a person.
"And what more can I ask for than to be with the best club in the world, in a fantastic city and with my family close by? I love it here and if they offer to renew my contract for life, I'd jump at the chance."
"I know I need to earn a few more stripes and I'm more than happy to accept that challenge. I've been here for seven years and I've absorbed the values of this great club by playing alongside legends like Zinedine Zidane and Raul," he added.
"Now I'm sharing the captaincy with Iker Casillas and I have to set an example and help the newer players, who don't know the club so well."