The Providence Journal reports the Patriots are not in the running and instead GM Scott Pioli and the Kansas City Chiefs are in pursuit. Smith, 27, is 6'3", 308 pounds and has only played in a 3-4 defense in his career.
The Broncos didn't offer him a tender putting him out on the market.
The Boston Herald reported that the Patriots and several other teams were interested in him at the start of free agency.
Smith would appear to provide depth along with Alex Magee behind Glenn Dorsey and Tyson Jackson.