In recent days, reports came out that linked Beckett to the Rangers and the Atlanta Braves. Earlier on Monday, the Braves were ruled out of the running for Beckett. The issue for Atlanta was the size of Beckett's contract, even if the Red Sox agreed to assume a large part of the $37 million left on the right-hander's contract which expires in 2014 (via WEEI). His original deal was for $68 million over four seasons.
It was assumed that Beckett would waive his no-trade clause to join either club. Beckett is 5-9 this season with a 4.57 ERA. The MLB trade deadline is July 31 but it does not seem likely Beckett will be traded at this point.