The 24-year-old defender had been expected to be utilised by new Real Madrid boss Jose Mourinho as a centre-back as he aims to bring in Maicon from Inter Milan for the right side of the defence.
However, reports in Spain claim that Chelsea are willing to lodge a €30 million offer to snare Ramos, who is part of La Furia Roja's squad for the World Cup in South Africa.
It is believed that Mourinho is reluctant to part with Ramos, but the Spaniard's sale could pave the way for the signing of Juventus' Giorgio Chiellini, a top target for the Special One, according to recent speculation.
Ramos has been with the Merengues since 2005, when he completed a €28m move from Sevilla.