The France defender, 33, reportedly wants to return to his homeland this summer having entered the final year of his contract in north London.
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He was expected to be part of the squad flying to the USA on Thursday – but Arsenal confirmed Koscielny refused to travel.
“Laurent Koscielny has refused to travel to the US for our pre-season tour,” a short statement on the club’s official website read.
“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.”
Campbell, who began his career with the Gunners and also went onto to play for a host of clubs such as Everton and West Brom, told his former side to fine the Frenchman and sell him.