A Milton Bradley–Pat Burrell swap is still a "strong possibility," according to Joel Sherman of the New York Post. Sherman notes that since Burrell is owed $9MM over one year and Bradley $21MM over two, the Cubs would have to eat good money (he guesses $6MM) to make the trade work.
There is no question that the Cubs would have to flip Burrell in this scenario. Sherman speculates that they could offer him to the Mets for Luis Castillo, a player the Cubs wouldn't mind adding. Sherman says, "It is hard to find a baseball official who actually thinks the Mets are going to land either Jason Bay or Matt Holliday," though ESPN's Buster Olney found one today in regard to Holliday.
My guess is that the Cubs would prefer to get a more usable piece than Burrell for Bradley. Acquiring Burrell increases uncertainty and drags out the process. Acquiring another bad contract more directly, someone they can use in center field, the rotation, or second base, would be ideal.