The Gunners brought in one new centre-half during the summer in Sokratis Papastathopoulos but have still had problems keeping clean sheets this season, prompting the club to consider other options.
With Shkodran Mustafi's future at the Emirates Stadium still in doubt and Laurent Koscielny working his way back from an Achilles injury, coach Unai Emery could do with an extra body in the heart of his defence and Bailly is the latest name to be linked with the spot.
The Mirror claims Bailly could be looking to leave United during the next transfer window should Jose Mourinho remain in charge, having become fed up with life under the Portuguese coach.
Bailly has started five games this season for the Red Devils but was hauled off by Mourinho after just 19 minutes of Saturday's 3-2 win over Newcastle after his team had fallen two goals behind.
The Ivory Coast international cost United £30million when they signed him from Villarreal in 2016 and the Manchester giants are likely to want significantly more than that should they decide to sell.
The reports claims Tottenham are also watching Bailly's situation closely, with boss Mauricio Pochettino known to be a fan of the 24-year-old.