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The 30-year-old’s future looked in doubt after he was relegated to an impact substitute under Arsene Wenger during the season that just finished.
However, the French international striker is ready win back a regular starting berth, as well as target more silverware.
“I am not insensitive to the approaches of the French clubs and especially that of Marseille,” he told Telefoot, as reported by the Daily Telegraph.
“But my future is in the Premier League. I still have titles to win.
“After the FA Cup, we will go for the league title. That’s my goal.”
The Frenchman currently has two years left on his Arsenal contract and is expected to remain in North London beyond the summer.
Since joining from Montpellier, where he won the Ligue 1 title, in 2012 he’s featured 227 times under Wenger managing 99 goals and creating a further 41.
Across the 2016/17 season he’s made no fewer than 40 appearances but still retaining that prolificacy in front of goal as he’s found the back of the net 16 times with 12 of those coming in 29 league outings.
Giroud is so far enjoying the current international break, having scored a hat-trick in France’s recent 5-0 win over Paraguay, which brings his overall tally for Les Bleus to 26 goals which places him among his nation’s top 10 all-time goalscorers.