The release of Allen clears $7.3 million in cap space.
The Patriots do have interest in bringing back Allen but at a lesser salary.
Allen, 29, played 13 games, with eight starts, and made only three catches for 27 yards in 2018. In two seasons with New England, Allen made 13 catches for 113 yards and a touchdown.
Andrews, 23, signed with New England as a rookie free agent out of UCLA last May. He spent the season on the reserve/non-football injury list.