The News of the World says the Ivory Coast midfielder, 25, was the subject of discussions when City's top officials met with Barca chiefs in Spain.
City chief executive Garry Cook denied the meeting was to set up a deal for striker Samuel Eto'o and was more a bridge-building exercise between the clubs.
But Toure's name was discussed and City are keen to tie up a transfer in the summer.
A Spanish source said: "City made a move for Toure in January but the player wanted to stay. But he is now willing to consider a move to City."