The France international has struggled for goals since helping his country win the World Cup in Russia in the summer, and has netted just once for the club in the league this season.
The Blues are set to offload fellow striker Alvaro Morata to Atletico Madrid imminently, but on Wednesday the club finally closed on a long-anticipated deal for Juventus striker Higuain – and that has plunged Giroud’s future at Stamford Bridge into doubt.
"I will never make people unanimously satisfied with me,” admitted Giroud in an interview with French broadcaster Canal recorded shortly before Higuain’s move was confirmed.
“There is a little part of regret and frustration. The public expects a goalscorer to score goals. I'm the fourth best goalscorer of French football and nobody can take that away from me.”
Chelsea boss Maurizio Sarri has used Eden Hazard as a central striker at times this season, an indicator of the manager’s deteriorating faith in both Giroud and Morata.
And the signing of Higuain may usher in the end of Giroud’s seven-year stay in England.
"The coach makes Hazard play nine which is detrimental to strikers,” said the Frenchman. “But he is the best player I've ever played with.
"If the club decides to get another striker, like Higuain, it will certainly darken my future at Chelsea.
Higuain made his debut during Chelsea’s 3-0 win over Sheffield Wednesday at Stamford Bridge on Sunday evening.
Two goals from Willian and one from want-away striker Callum Hudson-Odoi were enough to ease the cup-holder past the Championship side and into the fifth round of the FA Cup.
It remains to be seen whether it will be Hudson-Odoi’s final game in a Chelsea shirt, with the striker reportedly been on taking Bayern Munich up on their offer to bring the 18 year-old to the Bundesliga.