Balfour is an older, middle relief pitcher that is stating he wants a multi-year deal. The Rays are probably hesitant to sign him to a multi-year deal and simply do not have the money to sign him. The market is very small right now for middle relief pitchers like Balfour with his age and price tag, but there are always teams out there that need pitching, such as Boston, Philly, among others.
I am sort of sad to see Balfour leave the Rays. He was one of the more reliable pitchers for the Rays pen staff and now the Rays will have to go out and find another arm, which may get harder and harder.