Boro now have permission to speak to the 28-year-old and will hope to agree terms quickly so that he is available for Saturday's opener against Reading.
The Frenchman has refused to sign a new contract over the summer, so reluctantly manager Stuart Pearce has agreed to his departure, after spending four seasons at City.
After a season on loan at Newcastle he was purchased by Kevin Keagan at City for £4m from PSG.
There is no further news on the bid for Brett Emerton from Blackburn.