President Aurelio de Laurentiis told reporters City were not prepared to meet a £54m buy-out clause for the highly-rated striker.
"Manchester City do not have money to pay for Cavani because they say we won't pay that," De Laurentiis said on Friday.
"Abu Dhabi (City's owners) say they would never pay 63m euros (£54m) for Cavani."
And De Laurentiis believes his departure is far from inevitable.
"With Edinson nothing has changed," he added. "Headlines I've read in the papers did not represent his words exactly.
"He knows that he has a contract and an obligation to us, and there is a buy-out clause.