It is understood that a six-year contract is on the table, on improved financial terms.
It is also claimed that a buy-out clause will be placed in the contract meaning any interested party would have to part with €100million (£85m) in order to land Ramos.
The 24-year-old World Cup winner has been at Santiago Bernabeu since 2005 and has matured into one of Europe's top defenders during that time.
He has regularly expressed his commitment to Real over recent times but is keen to steer clear of contract talk for now.
"That is an issue for my agent," he told reporters when pressed on whether a new deal was imminent.