The 53-year-old is believed to head a list of possible successors for Arsene Wenger, whose current contract at the Emirates Stadium is set to expire in 2014.
Arsenal owner Stan Kroenke remains hopeful that Wenger will remain in north London for a further season - taking him to the end of 2014/15 - but has already held preliminary talks with chief executive Ivan Gazidis to draw up a shortlist of contenders.
Low's reputation for developing young talent and playing a stylish passing game make him well suited to the Gunners, having drawn plenty of plaudits for his work with the German national team, since he succeeded Jurgen Klinsmann in 2006.
Having taken his country to the final at the European Championships in 2008, Germany also made semi-final appearances at both the 2010 World Cup in South Africa, and last year's Euros in Poland and Ukraine.
Arsenal fans' only concerns might be Low's relative inexperience in club management, with his last job with Rapid Vienna ending in 2004. His greatest achievement came with Stuttgart back in his homeland, when he took the Bundesliga outfit to the Cup Winners' Cup final - which they lost to Chelsea - in 1998.
Low's current deal with the German football federation expires after next year's World Cup finals in Brazil, paving way for a potential return to club football with Arsenal ahead of the 2014/15 campaign.