French newspaper Le 10 Sport claims City are very interested in the Spain international, and would be willing to put together a lucrative package in excess of his current Real Madrid weekly wage to bring him to the Premier League.
The Bernabeu giants are reluctant to lose Ramos though, widely regarded as one of the world's best defenders.
So while City may be able to meet Ramos's personal demands, it remains to be seen whether Madrid president Florentino Perez will be willing to negotiate the sale.
One factor in City's favour is Ramos's reported desire to renegotiate his current pay packet - the centre-back wants fresh terms reflecting his senior status at one of the world's biggest clubs.
The 27-year-old is under contract until the summer of 2017, but Madrid could consider a sale if contract negotiations lead to a standoff between club and player.
Ramos fell out with Jose Mourinho last season, and he publicly questioned the decision to sell Mesut Özil to Arsenal on transfer deadline day.
The report claims he's unsure over the direction of the club under new boss Carlo Ancelotti, adding fuel to speculation that Perez may feel Madrid are better off without the centre-back next summer.
City have struggled with injury problems in defence, and were linked with Porto's Eliaquim Mangala earlier this month.