The Italy international fell out with his new coach after speaking of his frustrations at the uncertainty of his future at the Stadio delle Alpi.
Ranieri has responded by accepting Manchester City's bid for the 22-year-old left back, and admits that Chiellini may not return to the Turin club after their pre-season tour.
Ranieri said: "Will he come back to Turin with us? It will depend on him, Manchester City and Juventus.
"He is an important player, but if he does want to leave that we surely won't keep him against his will."
City manager Sven-Goran Eriksson is also after another Juventus player, Manuele Blasi, but there has been no word yet as to whether the midfielder will follow his team-mate out of Turin.