This opens a three-week window of time for the Patriots to activate them from injured reserve and add them to their 53-man roster.
Andrews missed the 2019 season due to blood clots in his lungs, but received medical clearance to return this past May.
Andrews, 28, wound up signing a three-year, $1.59 million contract with the Patriots as an undrafted free agent out of Georgia back in 2015. He was in the final year of his rookie contract when he agreed to a four-year, $9.615 million contract back in 2017.
Andrews is entering the final year of his four-year, $6,515,000 contract and is set to make a base salary of $3 million for the 2020 season.
In 2019, Andrews has appeared in two games for the Patriots, starting both at center.
Allen, 28, is a former seventh-round pick by the Eagles in the 2014 NFL Draft. He played out the final year of a four-year rookie contract worth $2,282,248 before agreeing to a three-year, $15 million contract with the Buccaneers in 2018.
Allen agreed to a $1 million pay cut last offseason that voided his $5 million base salary for 2020. From there, he signed a two-year contract that carries a max value of $8 million with the Patriots.
In 2019, Allen appeared in 13 games for the Buccaneers and recorded 10 total tackles, two tackles for loss, and 0.5 of a sack.