While he cannot formally sign for Atletico until January, Costa is training with his new club and will not play for Chelsea again after the two sides agreed a transfer worth up to £57.2million.
Former Blues boss Ranieri, meanwhile, has cast doubt on Alvaro Morata as a readymade replacement. The Italian believes Morata still faces a bedding in period.
“The first is a leader, he carries the team on his shoulders and plays with anger, with force and sheer will. The other is more of a dribbler.
“When you change your centre-forward, you have to also change your approach.”
Ranieri managed the Blues between 2000 and 2004.