Tiago's move to Lyon has been thrown into doubt after the French club accused Chelsea of increasing the fee.
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."
On Tuesday, Chelsea boss Jose Mourinho seemed convinced Tiago was on his way out of the club.
"It's a question of only a few details," he said.
"He provoked a lot of tears when he left on Monday because he's a wonderful boy and was a very good player for us.
"But he had a good offer from Lyon and their offer to Chelsea is very good. He wants to go and we couldn't break the legs of a boy like this to stop him."
Mourinho brought Tiago to Stamford Bridge on a four-year contract in July 2004.
Tiago made regular appearances for Chelsea last season, playing in 34 of the 38 league games and scoring four times, but is down the pecking order after Essien's arrival.