Allen, 25, wound up signing on with the Patriots as an undrafted free agent out of Louisiana Tech back in 2013.
Allen had one year remaining on his rookie contract and would have made a base salary of $585,000 for the 2015 season.
In 2014, Allen was 12th in the NFL in net punting at 39.9 and had 25 punts downed within the 20-yard-line. Pro Football Focus has him rated as the No. 31 out of 37 qualifying players.