In an article from Armando Salguero of the Miami Herald (found here), Salguero suggests the Miami Dolphins may take a serious run at Eric Mangini to be their general manager. Salguero discusses Mangini as someone owner Stephen Ross actually wanted to make a move like this back in 2011 but was rebuffed by Jeff Ireland and Tony Sporano. Salguero is presenting this as more of a musing than a matter of fact, but apparently this was considered in the past, so it could conceivably happen.
Mangini is currently a consultant for the San Francisco 49ers who basically comes up with ways to test the 49ers offense. He had been working with ESPN is presumably waiting for a more attractive position to open for him. He had been the head coach of the Cleveland Browns where he had some less than stellar results with the NFL Draft.
Mangini was able to draft Alex Mack who has been a good center for a number of years, but the 2009 draft, specifically the second round, was a series of awful decisions. Brian Robiskie, Mohamed Massaquoi and David Veikune were the three picks they had in that round and Massaquoi has probably had the most success of the bunch. It remains to be seen how seriously the Dolphins would actually consider this move, but stranger things have happened.