The 38-year-old was in attendance during Toulon's recent Top 14 win over Brive and is expected to join Jonny Wilkinson at the Stade Felix Mayol.
Wasps claim Shaw signed a new deal at Adam's Park earlier this autumn but has since decided to turn his back on that agreement.
The former English and European Champions have today released a statement making their feelings on the matter clear.
"Simon Shaw signed a contract extension with London Wasps in August, before leaving for the Rugby World Cup with England," read the statement.
"Simon requested that the club did not announce this at the time for personal reasons, which the club was happy to comply with.
"Upon his return, he informed the club last week that he would like to finish his career overseas. The club are very disappointed with this news and await an official approach for the player."