Jose Mourinho signed the 19-year-old from Saint-Etienne in January, staying in Ligue 1 for the remainder of last season, and is yet to displace first-choice pairing John Terry and Gary Cahill in central defence.
But the France Under-21 international is confident that his chance will arrive and Zouma also has one eye on making the national squad when his country host the European Championships in 2016.
"When I was at Saint-Etienne and I didn't play, I immediately got upset. But I learnt," he told L'Equipe.
"Now there are senior players, stars in my position, and they are doing a great job. I take my time. I am learning besides those defenders. I know my time will come.
"Jose Mourinho told me: 'Raphael Varane, I made him start against Manchester City. You have to be ready to play at any moment'.
"I am using Varane and [Eliaquim] Mangala as role models. Nowadays they are in the French team and I hope to join them.
"Euro 2016 is an objective I set to myself. Even if it will be very difficult to get a position, the door is not so far away."