The Frenchman has reportedly emerged as a target for Ligue 1 side Marseille, per the Mirror's Neil McLeman. However, he has said he is not thinking about a return to France.
He told Dauphine Libere (h/t Naveen Ullal at Sport Witness): "I’ve heard a lot of things in the media… In the near future, my goal is not to return to France. For now, I’m a Chelsea player."
Giroud only arrived at Chelsea from Arsenal in January, signing an 18-month contract at Stamford Bridge.
He made an impact during his short time in west London and scored five goals. The 31-year-old ended the campaign as the team's first-choice striker and helped them win the 2018 FA Cup.
Giroud also played a key role in France's victory at the 2018 FIFA World Cup. Giroud did not score in any of his seven games, but he formed an important partnership with Kylian Mbappe and Antoine Griezmann in attack.
Giroud faces competition for his place in the Chelsea team under new manager Maurizio Sarri. Alvaro Morata disappointed in his debut campaign and lost his place in the side to Giroud.
However, he has said he will stay at Chelsea and has been told the club have confidence in him, per Darren Lewis at the Mirror.
The Spaniard will need to turn his form around to get into the team, according to Goal's Nizaar Kinsella:
Michy Batshuayi is also back at the club after spending last season out on loan at Borussia Dortmund.
Sarri is willing to make the Belgium international a key part of his team, per the Evening Standard's Simon Johnson.
Tammy Abraham is another option after returning from a loan at Swansea City. However, he may spend another season away from the club, per Kinsella:
Sarri is expected to adopt his preferred 4-3-3 formation this season and use one striker flanked by forwards Eden Hazard and Willian.
The Italian will have decisions to make over whether to use Morata, Giroud or Batshuayi, but the Frenchman should still see plenty of game time next season if he does stay.
Morata may start the season as the team's first choice as Giroud and Batshuayi will have returned to the club later due to their World Cup exploits.
Giroud will turn 32 in September, but he's a proven Premier League striker, is strong in the air and is an excellent option coming off the bench. While he may not be the future for Chelsea, he still has the quality to play a role next season.