The France international has found himself behind Morata in the opening five Premier League fixtures of the 2018-19 season so far.
The former Real Madrid striker has scored one goal in four starts in the English top flight after Morata found the net in a 3-2 win over Arsenal.
Giroud, on the other hand, has only started one Premier League game and has been limited to three substitute appearances so far.
While the ex-Arsenal striker hasn’t found the score sheet so far this term, Giroud has made three assists to help the Blues make a positive start to the campaign.
However, the Chelsea FC striker is relishing the battle for a starting spot with Morata, adding that their rivalry can help fire Chelsea FC to silverware.
“It has always been a fair competition between us and we will both try to step up to help the team reach our target,” Giroud told the Evening Standard.
“I didn’t play at the beginning of the season because I came back late from the World Cup. I had to be patient, I had to reach a decent physical level.
“The coach said he wouldn’t make many changes until the end of August. He was clear about that. Alvaro did well at the start, he did all the pre-season. It was fair he started the season.
“I’m happy to have a team-mate like that, who pushes me to do better. It’s positive for both of us. I want to play as many games as I can and try to be as efficient as I can for the team.”
Chelsea FC were 4-1 winners against Cardiff City in the Premier League at Stamford Bridge last weekend.
The Blues finished in fifth spot in the Premier League table last term to miss out on a Champions League place.
The west London side appointed Maurizio Sarri as their new manager in the summer.
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