The 31-year-old warns the Atletico Madrid loan star and Belgium international that he is not ready to relinquish his position as the Blues' first-choice goalkeeper
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Cech told Goal: "In big clubs you always have competitions for places. Obviously every player wants to keep their spot in the starting line-up and I'm the same. We will see.
"When you start pre-season everybody fights from the same line and you need to do well in the pre-season to persuade your manager that you deserve to be on the pitch for the first game. It's always up to you and your performances how you persuade the manager that you should play."
The Czech Republic international has been impressed by Courtois's performances for Atletico, however, praising his efforts in the Copa del Rey final as the Spanish side overturned local rivals Real Madrid.
"I watched the Copa del Rey final and, for most of the game, it looked like Real Madrid might win it," he observed. "They hit the post three times but then then they had chances in important times.
"Thibaut made great saves in extra time. That's what gave them a chance to win the cup."