Low is one of the names to have been mentioned in the discussion of Arsene Wenger's successor after it was revealed that the Frenchman will step down from his role following 22 years at the end of this season.
The 58-year-old Low has not worked in club management for 14 years, and The Times reports that he is worried he would not be able to carry out his duties effectively in the immediate aftermath of the World Cup should he take over the reins at the Emirates Stadium.
The long-serving Germany boss - who still has two years remaining on his current contract - took a lengthy break after leading his country to the 2014 World Cup title having been left physically and mentally drained, and his side will once again go into this summer's tournament among the favourites to lift the trophy.
Many of Arsenal's first-team players will return to training before the World Cup final takes place on July 15, while any new manager would be required to travel with the team to two International Champions Cup matches in Singapore the following week.
Such an intense schedule is likely to put Low off the job, leaving former Barcelona manager Luis Enrique as the most realistic high-profile candidate for the Gunners.