By Greg A. Bedard, Globe Staff

PALM BEACH, Fla. - The Patriots are finalizing a contract with former Cowboys fullback Tony Fiammetta, according to a league source.

UPDATE: Fiammetta agreed to terms, which weren't disclosed.

Fiammetta, 25, would give the Patriots three fullbacks on the roster. Lousaka Polite finished the season with the team after being brought in mid-season, and the Patriots recently signed former Broncos fullback/linebacker Spencer Larsen.

Apparently, new offensive coordinator Josh McDaniels is aiming to run a little bit more of a two-back offense, which was largely non-existent under Bill O'Brien outside of short yardage.

The Cowboys elected not to tender Fiammetta as a restricted free agent for $1.26 million. They attempted to sign him to a contract extension at less money, but Fiammetta elected to test the market. The Cowboys signed Lawrence Vickers instead.

Fiammetta was drafted in the fourth round of the 2009 draft by the Panthers out of Syracuse. He battled concussions in Carolina, which led to his release in September.

Fiammetta played well for the Cowboys last season before a mysterious ailment -- later revealed as an inner-ear infection that caused balance issues -- caused him to miss three games. Fiammetta wasn't quite the same player when he returned, but the Cowboys' running backs enjoyed much more success when he was on the field compared to when he was off it.