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The 10-cap Germany international has 16 goals in 29 appearances this season, adding to the 21 struck last time out when finishing fourth in the Bundesliga scoring charts.
Werner has already been linked with Chelsea, Manchester United and Liverpool in the past, and The Sun suggests that the Gunners are now ready to make a move.
Arsenal are said to have sent scouts to watch Wernger in action against Napoli on Thursday evening, with the 21-year-old – who has rejected the offer of a new deal at Leipzig – scoring in the 3-1 win.
Real Madrid and Atletico Madrid have also been touted as possible destinations for the German, but his current club remain determined to keep hold of him.