Gunners management have had concerns about the attacking options to manager Mikel Arteta this season and have plans to bring in a young forward over the summer.
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BILD's Christian Falk is reporting Arsenal are currently favourites to sign Tresoldi, 21.
Talks about a transfer have already begun, with Arsenal considering the player for both the present and the future.
Tresoldi, born in Italy, is a Germany U21 international and has a deal with Club Brugge to 2029.