The 19-year-old claims the Stamford Bridge boss contacted him in December and adds he is looking to leave Saint Etienne in the summer, possibly to move to west London
Zouma, 19, has established himself as one of the most promising young centre-backs in Europe with a series of impressive performances in Ligue 1 and in various France youth sides.
But he claims he has an agreement with his club which will allow him to move on at the end of the season, and says his contact with Mourinho has made him more favourable towards a switch to Stamford Bridge.
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“When a great man like Jose Mourinho calls a little player like Kurt Zouma, it’s nice. It doesn’t happen every day and it’s a big sign of respect and confidence.
“If you tell me to go to Chelsea, I’ll go there immediately! Especially after the call from the coach. It’s given me ideas.
“I’m playing my third season in Ligue 1,” he said. “In June, it will be time to go and see how things happen elsewhere.”
Yet despite the Blues' advances, Zouma insists he is keeping his options open and has not ruled out remaining in his homeland or going elsewhere on the continent.
“Why not a step up in France? For me, Saint-Etienne are already a big club,” he added.
“But after that, the top teams are Paris Saint-Germain and Monaco. It would be a good career plan. Abroad, it’s make or break. But it’s a risk worth taking.
“I won’t necessarily choose according to the league. It will depend on playing time and the state of mind of the coach and the squad.”