The News of the World says the Eastlands club agreed to meet his buyout clause at Benfica, which would trigger a record British transfer fee.
But Di Maria, 21, declined a move that would have beaten the previous record of £32.5m City paid Real Madrid for Robinho.
Undaunted, City are certain to be back in the summer for the player, who rejected a switch this month as he wants to help Benfica win the title.
A source in Lisbon said: "City offered the amount required to trigger a release clause in Di Maria's contract but the boy is loyal to Benfica.
"But everyone at Benfica accepts that he will move on sooner rather than later."