The Daily Express says reports suggest Arsene Wenger is ready to spend £20m on Gundogan, who spearheaded Dortmund's charge to the Champions League final last season.
It is also understood that the 22-year-old is being eyed as a long-term replacement for Mikel Arteta, who turns 32 next year.
Gundogan's father, however, feels a move to Arsenal could come too son for his son.
"He is doing fine so it's a bit early to move to a club in England or Spain at this point in time," he said.
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