The French striker has scored some crucial goals for the Blues this season - including against Wolves to help them seal a place in next season's Champions League - but his prospects at Stamford Bridge have been placed in doubt by the capture of Werner from RB Leipzig.
Giroud, however, remains unfazed by the added pressure.
The 33-year-old forward told L'Equipe newspaper: "When the teams play a defensive way against us, it's not bad to have a tall striker like me that can make the link. But I am not naive.
"Werner hasn't been recruited to sit on the bench. But I will do everything I can to give headaches to the coach when it comes to making his choice."
Giroud admits that he was "expecting" Frank Lampard to sign a centre forward to strengthen the side for next season.
He said: "Werner's transfer is an additional motivation and it was inevitable that the club recruits a striker.
"Chelsea is a great club, that spends money to strengthen the squad, and I was expecting someone to come."
The World Cup winner suggested that he is keen to extend his career at the London club after his contract expires next year.
Giroud said: "I still have a year of contract here. If I stay here afterwards, that's fine. Otherwise, it will be another challenge.
"But I can still play in a good league for two years. I don't set any limits."