From my perspective, this could be about Belichick wanting to see a player succeed even if it is not as a member of his team. If the Patriots retain Edelman, which appears to be their desire then Amendola most likely would become the #3 or #4 receiver on this team, is that really in the best interest of Amendola? Belichick and Kraft likely made a commitment to Amendola that he would be a starter when he signed here last offseason, if Edelman is here they will not be able to uphold that commitment so they are likely trying to do right by Amendola and find him a place that can, while helping the team at the same time.
Belichick has always attempted to let coaches and players that were under him go to places that gave them the best opportunity to succeed, he has never held a player back for the sake of hording talent. Bledsoe, Cassel, and others have all been examples of this, even McDaniels this season with the Browns opportunity, Belichick never holds people back.
If you are a fan of Amendola, do you really want to see him as a fourth receiver? I am not even a huge fan and I would prefer to see the guy get an opportunity to go someplace where he can meet his max potential.