Last season, Amendola caught 61 passes for 659 yards and scored two touchdowns.
Along with the Patriots, the Dolphins are also in the AFC East.
Amendola, 32, will best be known for his playoff performances in his five seasons with New England. When the financial figures are released, it might be easier to understand why they declined to match the offer for a player who couldn't fill a fulltime role for the length of the year.
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Losing Amendola has a minimal effect on the Patriots offense - in the regular season. The big move that preceded Miami's trade of Landry and expected release of Suh to the Cleveland Browns was acquiring Robert Quinn, who hasn't been dominant in two seasons. In his career as a Patriot, he has 230 receptions for 2,383 yards, and 12 touchdowns.
While Amendola and Wilson are both best utilized as slot receivers they each have experience playing on the boundary, which could help them fit in well with DeVante Parker and Kenny Stills, Miami's returning starters.
Contracts are not official until 4 p.m. Wednesday, but if the deal indeed goes through, he would become the second receiver to sign with the Dolphins this offseason.