The Gunners are in desperate need of defensive reinforcements after struggling at the back last season.
Mustafi was regularly criticised for his underwhelming performances while Koscielny has not looked the same player since returning from an Achilles injury.
Unai Emery has limited transfer funds this summer and has so far prioritised a pursuit of Crystal Palace star Wilfried Zaha.
But he may need to turn his attention to a new centre-back after Koscielny refused to join his team-mates on their pre-season tour of America.
The Frenchman wants to force through a move away and his exit could leave Arsenal short of numbers at the back.
According to BBC Sport, the north London side are also keen to sell Mustafi.
But the report claims the German has no desire to leave.
Mustafi is under contract at the Emirates until 2021.
“We are very disappointed by Laurent’s actions.”
Reports suggest Emery has a transfer budget of just £45m this summer, meaning he must sell to finance his key targets.
Koscielny’s situation could force them to bring in two centre-backs to rival Sokratis Papastathopoulos and Rob Holding.
Arsenal released a statement yesterday confirming their captain’s absence from their tour.
“Laurent Koscielny has refused to travel to the US for our pre-season tour,” it said.
“We are very disappointed by Laurent’s actions, which are against our clear instructions.
“We hope to resolve this matter and will not be providing any further comment at this time.”
Arsenal are also targeting a new left-back to replace Nacho Monreal.
Celtic’s Kieran Tierney appears to be their No.1 target but speculation has gone quiet after Arsenal were quoted £25m.