The report suggests that Arsenal see Amiri as a long-term replacement for his fellow countryman Mesut Ozil, who is expected to leave the club this summer.
Tottenham are reportedly leading the race to sign the youngster after missing out on a deal in the summer transfer window.
Amiri has scored just four times and registered two assists in all competitions this season, but he played a key role in Hoffenheim’s success under Julian Nagelsmann last season.
The 21-year-old is yet to make his first senior appearance for the German national team but he was part of the 2017 U-21 European Championship winning squad.
Hoffenheim currently sit seventh in the Bundesliga table.