In a statement the Premiership side say the England international requested news of his new deal remained private until he returned from World Cup duty.
Shaw, 38, who has 71 international caps, featured three times for Martin Johnson's side in New Zealand.
"Upon his return, he informed the club last week he would like to finish his career overseas," the statement read.Continue reading the main story Born: 1 September, 1973Position: LockJoined Wasps from Bristol in 1997, going on to play 339 times for the High Wycombe-based clubIn 2009 he became the oldest player to be capped by the British & Irish Lions, lining up against South Africa aged 35His replacement appearance in the World Cup quarter-final loss to France was his 71st England cap
"The club are very disappointed with this news and await an official approach for the player."
The statement added that the former British & Irish Lions forward, who has played 339 times for Wasps since joining from Bristol in 1997, had asked that his new deal be kept under wraps for "personal reasons".
"Simon requested that the club did not announce this at the time for personal reasons, which the club was happy to comply with," it read.
Shaw's desire to leave follows the news that head coach Shaun Edwards has parted ways with the Adams Park club.