Allen signed a four-year, $29.4 million deal last spring to remain with the Colts, but the former third-round pick (2012) was made expendable due to the emergence of Jack Doyle in 2016. Doyle signed a contract with the Colts last week.
The Patriots could lose Martellus Bennett in free agency and Allen is capable of being a full-time starter in a system that often uses tandem tight ends -- provided Rob Gronkowski recovers from a second back surgery.
The move is not official until Allen passes a physical and trades cannot be finalized until Thursday at 4 p.m. ET, when the new league year officially begins.
Allen is due $4.9375 million in 2017 and $5 million in 2018 before the deal jumps to $7.4 million in 2019.