Havertz could take Fullkrug's place in Germany's attack at the Euros given his form in the No9 role with the Gunners.
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But the BVB centre-forward says: "I wish Kai every goal so that he can take us forward significantly as a team and as a country.
"We have a unique opportunity because we are playing this European Championship at home and we have to do well.
"As far as I'm concerned, I have to identify with my role and at the same time time to work in training to make sure I have more space to play."