Butler would have to sign his restricted free agent tender to be traded and he hasn’t done that yet, but the Saints can still sign him to an offer sheet. The Patriots would have a chance to match and would get a first-round pick back from New Orleans if they chose not to match.
If that’s going to happen, the first step in the process will apparently take place on Thursday. Saints coach Sean Payton told Brett Martel of the Associated Press that Butler will visit the Saints that day.
The Saints have the 11th and 32nd picks in the first round with the latter coming from the Patriots in the deal for Cooks. The higher of those picks would be handed over if they signed Butler as a restricted free agent, although the two teams could potentially work out another arrangement if Butler signs his tender as part of the process of landing a long-term deal with the Saints.