While this shouldn't come as too much of a surprise to anyone, according to Jon Heyman, the Red Sox looked into trading Jonathan Papelbon earlier in the offseason.
Heyman specifically cites the Athletics and White Sox as potential landing places for Papelbon, but says that the high price tag arbitration was likely to bring kept the teams at bay. Papelbon received $12 million on Tuesday, coming to an agreement with the team on a one-year deal. Whether a lower salary could have been achieved in arbitration, we'll never know.
Rafael Soriano would have been the replacement for Papelbon if the Red Sox had been able to trade him. In fact, it seems like both parts of any deal would have been dependent on one another. The Sox would not have traded Papelbon if they couldn't sign Soriano, and likely would not have signed Soriano if they couldn't find some way to unload Papelbon.
What does seem clear is that the Sox were not willing to commit nearly as many resources to Soriano as the Yankees, who signed their new setup man to a 3-year, $35 million dollar deal. It's unclear just how high they would have been willing to go, but having already signed Type-A free agent Carl Crawford, the Sox only stood to lose a second round draft pick.