I believe that a team signing Monroe loses his Bird rights, meaning that the most we can give him is 120% of his current salary. His salary is around $5.5 million, so if we traded for him, we could sign him to a contract starting around $6.6 million next year.
That's not going to get it done. Now, if we clear significant cap room, we don't have to rely upon an exception to sign him, and can just use cap space. However, that's a possibility with or without a trade.