The Senegal striker, who joined the Blues from Newcastle United last month, has shared the forward role with Fernando Torres since moving to Stamford Bridge.
However, he told The Sun: "Everywhere you go, competition is there. It will always exist. I'm at one of Europe's biggest clubs and, each year, they're going to bring in a striker. That's part of football. It's what makes you better if you take it the right way.
"I work, I know what I can achieve. If they buy a new forward, it'll help me improve. I won't let myself be pushed around."
The 27-year-old has scored three goals for Chelsea.