The Sun is reporting that the German club want to add to their attacking options in the summer transfer window and that they are targeting a deal for the 19-year-old.
Nelson spent last season on loan to German club Hoffenheim, where he scored seven goals in 25 appearances for the Bundesliga side.
Now, it appears that the youngster could be on his way back to Germany for another season if the move is approved by Gunners boss Unai Emery.
According to the same story, Emery will have the final say about whether Nelson is shipped out on loan again or if he will be kept at The Emirates for more of a regular run in the first team.
Arsenal are still thought to be on the lookout for a number of new signings this summer as they aim to strengthen their squad ahead of next season.
The Gunners finished in fifth place in the Premier League table last term and without a trophy – and they have so far signed Brazilian teenager Gabriel Martinelli.
Arsenal will kick off their Premier League campaign with a trip to Newcastle United on 11 August.
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