The 38-year-old has been heavily linked with a move to Toulon in recent days, with the French side thought to have gone as far as offering the 68 Test cap forward a short-term contract.
In a statement, Wasps said: “Simon Shaw signed a contract extension with London Wasps in August, before leaving for the Rugby World Cup.
“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.”
Shaw’s sudden change of heart represented a double blow to the London club who also confirmed the departure of long-serving head coach Shaun Edwards.
The 45-year-old had been part of the coaching set-up at Wasps for a decade but departs after discussions with the club after the conclusion of the World Cup, where he served as Wales’ defence coach.
Edwards’ future at the club had been in doubt after he recently revealed that he expected to return from the World Cup, where he helped Wales to a fourth-place finish, as a “free agent”.