Bordeaux have reportedly offered the Frenchman a three-year deal.
Arsenal defender Laurent Koscielny has refused to travel on the club's pre-season tour of the US.
The 33-year-old France international is out of contract at the end of the 2019-20 season and is a reported target for French clubs Bordeaux, Rennes and Lyon.
"We are very disappointed by Laurent's actions, which are against our clear instructions," said Arsenal.
"We hope to resolve this matter and will not be providing any further comment at this time."
Bordeaux have reportedly offered Koscielny a three-year deal.
The central defender joined Arsenal in the summer of 2010 for a fee of around £10m.
He has played 353 times for the Gunners and won the FA Cup twice in 2013-14 and 2014-15.
Last season Koscielny played 30 times for the club in all competitions, including one appearance for the under-21s.