The 28-year old England international was not offered a new contract by the Blues and will now be allowed to leave as a free agent.
Giesse admitted that Cole would have some time off following his World Cup duties and would then make a decision on his future which is pointing towards a move to either Tottenham or Arsenal although some Italian clubs are believed to be interested.
"For now there is no news," Giesse told calciomercato.com.
"The boy has just returned from South Africa and now he will go on holiday. There are clubs interested in him, we are talking about a world-class player.
"I think by the end of the World Cup there will be developments and within two to three weeks there will be some news.
"Several English clubs have asked for information, but at the moment nobody has moved concretely. After the World Cup we'll be going to reach conclusions."