Quoting reports from Spain, the Daily Express claims Arsene Wenger hopes to beat Barcelona to the signing of the Germany international, although Manchester City and Manchester United have also been linked with the Borussia Dortmund defender.
The report claims United and City have expressed an interest in bringing Hummels to the Premier League, and have actively sounded out his interest in joining their clubs, but neither have placed a serious bid for the centre-back.
The 24-year-old fits Wenger's profile when it comes to purchasing young players with potential sell-on value, and the Daily Express claims Hummels is high up on the Arsenal boss's shortlist.
Wenger is believed to be prioritising a new defender, as he think the Gunners need to strengthen at the back if they are to challenge for trophies in the next few years. The north London club have not won a major title since their 2005 FA Cup truimph.
Reports in Spain suggest preliminary talks may have already begun between Borussia Dortmund and Arsenal, but a potential stumbling block could be Hummels' asking price - believed to be £17.6m.
The Germany defender has started all of Dortmund's Bundesliga match this campaign, and was instrumental in last season's league title triumph.
Along with defensive partner Neven Subotic, Hummels has been one of the most impressive performers in the Bundesliga, and a key part of Dortmund's success in this year's Champions League.