The Blues are currently in fifth place in the Premier League table and seven points behind fourth-placed Tottenham with just five games left to play this term.
Their current position means it is unlikely that they will be able to break back into the top four this season, and they look set to have to settle for a place in the Europa League next term.
Giroud came off the bench to score two goals and inspire Chelsea FC to a dramatic 3-2 comeback against Southampton in the Premier League on Saturday.
And the January signing has insisted that he and his team-mates will not give up the fight for a top-four finish until it is mathematically impossible.
Speaking to Sky Sports after Saturday’s win, Giroud said: “As long as mathematically it is going to be possible, we are going to believe.
“So we take the games one by one and we have maybe five or six finals to play. Let’s do the job and we will see what the other teams do.”
Chelsea FC will take on Southampton in the FA Cup semi-finals on Sunday as they look to try and reach the final for the second season running.
Antonio Conte will be keen for his team to end a difficult campaign on a high by lifting the FA Cup trophy after having been beaten in the final by Arsenal last year.
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