The offer is not linked with the ongoing negotiations for David De Gea, according to Spanish newspaper AS Diario.
Ramos, was the subject of a £28.6million bid by United last month and now the Red Devils’ improved offer is believed to be their final attempt to sign the 29-year-old.
The Spain international’s exit from the Bernabeu is now seemingly inevitable as Real are struggling to meet the defender’s wage demands – Ramos wants £7million a year.
United are reportedly planning to offer Ramos an even better deal worth £7.6million which would rival that of striker Wayne Rooney.
However, Ramos may still be a Real Madrid player next season as the La Liga giants are determined to receive their full £62million asking price.
The United goalkeeper has been heavily linked with a move to Real Madrid and has already turned down a new long-term deal at Old Trafford worth £200k-a-week.
However, the Spain international may have to wait until next summer before he can move back to his homeland after United insisted they want a world record fee of £35million.
Earlier reports claimed the Red Devils were prepared to accept an offer of £25million for De Gea with Madrid only prepared to go as high as £15million for the 24-year-old.
But, a club source at Old Trafford later rubbished reports they would accept a £25million bid and insisted no formal bid had been as of yet.
Written by Jack Wynne – @JackRobertWynne