Giroud started just 11 Premier League games this past season as Arsene Wenger opted to deploy Alexis Sanchez as Arsenal's sole striker.
He had to wait until December to earn his first start of the campaign and went on to score in five successive games, including a goal in the FA Cup third round win over Preston.
His lack of opportunities in the starting line-up at Arsenal led to speculation that he could look to move on this summer.
Marseille had emerged as potential suitors to sign the France international.
Olivier Giroud has no plans to leave Arsenal this summer
Alexis Sanchez's future at Arsenal remains up in the air
But my future is in the Premier League
But Giroud insists he has no plans to leave the Emirates any time soon.
"I am not insensitive to the approaches of the French clubs and especially that of Marseille," he told Telefoot.
"But my future is in the Premier League. I still have titles to win.
Olivier Giroud linked with Marseille transfer Mon, April 24, 2017
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"After the FA Cup, we will go for the league title. That's my goal."
Giroud became the first player since David Trezeguet in 2000 to score a hat-trick for France in Friday's 5-0 win over Paraguay.
While Giroud claims he won't be leaving Arsenal this summer, the Gunners are yet to provide any update on Alexis Sanchez's future.
The Chile international has just one year left on his contract and Arsenal are keen to tie him down to a new deal but the two parties are at an empass over Sanchez's wage demands.