The 21-year-old is struggling to hold down a regular starting place under Jose Mourinho and the Gunners are hoping to capitalise on this uncertainty by taking the French international to the Emirates.
Two major obstacles stand in their way. The first comes in the form of FC Barcelona, who are also rumoured to be interested in the unsettled striker. Moving to one of the biggest clubs in Spain may appeal to him more than moving to a Premier League rival.
It will certainly appeal more to Jose Mourinho.
When the Portuguese was in charge at Stamford Bridge, Petr Cech was sold to Arsenal against Mourinho’s wishes because Roman Abramovich had given his word to the long-serving goalkeeper that he could stay in London when he left Stamford Bridge.
Mourinho strongly argued that the move strengthened a rival and demanded Abramovich renege on his word. It didn’t end well with Cech getting his wish while Mourinho got the boot.
Selling a striker to a rival is unlikely to happen this time. Mourinho dashed Demba Ba’s hopes of moving to Arsenal in 2013 on loan for the same reason.
Martial is likely to find Mourinho equally as stubborn.