The News of the World says Silva has already said 'no' to a five-year contract with City.
They are prepared to pay Silva a bigger salary than Chelsea but he wants to play Champions League football next season.
Their president Manuel Llorente said: "We have received calls about Silva but no concrete offers.
"Right now nothing is out of the question because we need to safeguard the future of the club."
Silva, 24, capped 33 times by Spain, has a release clause of around £28m but is likely to leave Valencia for around £20m.
His agent Amadeo Rengel said: "The option of Chelsea is the most interesting in terms of the sporting project."