The 24-year-old appeared to be on the verge of a £6.5m transfer after he and his agent travelled to France to discuss personal terms on Monday.
But Lyon president Jean-Michel Aulas told L'Equipe newspaper: "Tiago was the priority following the departure of Michael Essien to Chelsea.
"But we are a little bit irritated by the raising of the price."
Tiago played in 34 of the 38 league games and scoring four times last season.