Dortmund value the 23-year-old at around £27m, which is affordable for the Gunners as manager Unai Emery reportedly has a transfer budget of £45m to spend this summer.
The Bundesliga runners-up are allegedly happy to let Weigl go due to their recent capture of Mats Hummels from Bayern Munich, with Weigl falling down the pecking order at the club.
The Germany international, who has won five caps for his country, made just 17 appearances for Dortmund in all competitions last season, scoring once, and is not regarded as a key player to hold on to.
Arsenal may face competition for his signature, however, as Paris Saint-Germain have also been linked.
Weigl is also able to play in defence, and is the sort of versatile player Emery is looking for as he attempts to rebuild his squad this summer.
The Gunners have had a frustrating summer so far, with their limited transfer budget meaning they are unable to afford to bring in players of the quality they would like.
They recently had a £43m double bid for Sampdoria pair Joachim Andersen and Dennis Praet rejected, and are also struggling to get through a move for Yannick Carrasco from Chinese side Dalian Yifang.
Crystal Palace star Wilfried Zaha has also expressed his desire to join Arsenal, the club who he supported as a child, but Palace value the player at £80m, which is surely out of the north London club's price range.
With Aaron Wan-Bissaka reportedly close to sealing a move to Manchester United having travelled up to Manchester for a medical, Palace may also be doubly keen to keep hold of their fans' favourite.
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