Arsene Wenger has not given up on bringing Lars Bender to Arsenal this season and is keen to make an improved offer in January having seen Bayer Leverkusen reject a bid of £18.5m in the summer.
Having sold Andre Schurrle to Chelsea and Dani Carvajal to Real Madrid, Leverkusen were under no pressure to cash-in on Bender and immediately rejected Arsenal's offer.
However, the Daily Mail reports that Wenger is still interested in signing the Germany international and is prepared to make an offer of £20m as he seeks to further improve his squad during the winter transfer window.
The Gunners boss has a core of German players in his ranks with Lukas Podolski, Mesut Ozil, Per Mertesacker and Serge Gnabry all excelling at the club, and may well hope that they could prove key in persuading Bender to make the move to north London.
The 24 year old is in his fifth season with Leverkusen who will be hoping to keep hold of one of their most instrumental players. Sami Hyypia's side have made an impressive start to the season, winning six and losing just once to sit third in the league behind Bayern Munich and Borussia Dortmund.
With Leverkusen competing for major honours both domestically and in Europe, it may well be difficult for Wenger to persuade the club to part with the midfielder unless he decides it is time to leave the club.
Bender has seen his twin brother Sven enjoy plenty of success with Dortmund in recent seasons, while Leverkusen have failed to win any silverware in his time at the club.
While Wenger is said to see Bender as a replacement for Mikel Arteta, he may face competition from Manchester United who are also said to be interested in signing the 24 year old.
Bender played against United in the Champions League earlier this season and David Moyes is said to be keen on landing the midfielder after a dreadful start to the season.
United have made their worst ever start to a Premier League season, culminating in the 2-1 loss to West Bromwich Albion at Old Trafford on Saturday.