The France international has been limited to a string of substitute appearances following his £10.5m move to the Blues from Queens Park Rangers in the summer transfer window.
Costa, who joined Chelsea in a £32m deal from Atletico Madrid this summer, has already scored nine goals in seven Premier League games.
But Remy, 27, is refusing to be discouraged as the former Newcastle United forward looks to impress Jose Mourinho and forge a successful Chelsea career.
“When opportunities like this happen, you can not refuse. It happened late in life,” Remy told the Daily Star.
“In my head, I quite wanted to stay at QPR, but I did not hesitate for one second for many reasons.
“The move was for my improvement, for my confidence, in terms of level of demand. Chelsea is one of the best clubs in the world. I’m happy to have signed for a club like this. I know I’m not going to be the first striker, but nothing is set.
“I have goals. By signing at Chelsea, I did not say it was to stay on the sidelines. I will try to move up alongside great players. The rest will happen naturally.”
Remy scored his first Chelseaa goal in a 4-2 victory over Swansea City.
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