The 19-year-old centre-half has long been linked with a switch to Stamford Bridge, and the Blues appear to have stepped up their chase.
Zouma is not expected to be on the move in January, but claims to have an agreement with his current employers which will allow him to take on a new challenge in the summer.
It could be that he heads for England, with the youngster admitting that he would jump at the chance to join a Premier League heavyweight.
He told L'Equipe on the Chelsea links: "A phone call from Mourinho? It is true, there was contact a month ago.
"At first I thought it was a joke. When a great man like Jose Mourinho contacts a small player like Kurt Zouma, that offers great pride.
"If I was told to join Chelsea, I would go immediately. It will be down to the coach, though, to make the call."
Zouma, who has also been heavily linked with Serie A giants Inter Milan, added: "In Italy it is much more tactical. That helps you to improve a lot. In England it is much more physical.
"But I won't necessarily make a decision based on the league. It will depend on how much I will play, the coach and the group. I will take my time.
"I want a change. That is the agreement we have. I am playing my third season in Ligue 1 and it is the right time to go somewhere else.
"Going abroad will be make or break, but that is a risk worth taking."