Giroud, who only joined Chelsea in January from Arsenal, has been linked with a move away from Stamford Bridge.
Marseille are interested in bringing the World Cup winner back to France.
Recent reports had suggested that Giroud could leave to make way for Gonzalo Higuain.
However, a spanner was put in the works when Higuain opted to join AC Milan instead on an initial loan deal worth £16million.
While there have been question marks surrounding Giroud’s future, the player has confirmed he will be staying in west London.
“I’ve heard lots of things being reported in the media,” Giroud said.
“In the near future, my objective is not to go back to France.
“At the moment, I am a Chelsea player.”
Giroud won’t play any part in the Blues’ Community Shield clash against Manchester City later today (3pm) as he has only just returned to training.
Meanwhile, Maurizio Sarri believes he is one player short heading into the new season.
He said: “I think we need something. But only maybe one player.
“I spoke with the club about the market but only one time, no more.
“I spoke about positions but no specifics – no names – so I don’t know.”
The Premier League transfer window closes on Thursday.