Speaking on the official website McClaren said "We are disappointed that Mark has made this decision but respect his feelings.
"In the football club's best interests, we have agreed to his request and will listen to any offers we receive."
It's nine years ago this month that Schwarzer was signed by Bryan Robson from Bradford and he still has two years of a three year contract remaining, so Boro will expect a sizeable fee for the 33-year-old.