The Patriots are loaded at the top of the tight end depth chart with Rob Gronkowski and Bennett, followed by powerful blocker Michael Williams and 2015 sixth-round draft choice AJ Derby of Arkansas.
Last September, in preparation for the game against the Jaguars, Patriots coach Bill Belichick compared Harbor to Oakland Raiders fullback Marcel Reece.
"He's a fullback, tight end kind of guy, sort of lines up in a lot of different places," he said.
Harbor, 28, had 64 catches for 730 yards and four touchdowns in three seasons with the Jaguars.
He started 15 games and caught 50 passes in 2013-14 but the improved health of Marcedes Lewis and the addition of Julius Thomas slashed his production. He had just 14 catches for 149 yards and one touchdown in 2015.
Harbor played three seasons in Philadelphia before joining the Jaguars, catching 47 passes for 421 yards and four touchdowns.
ESPN's Mike Reiss and Michael DiRocco contributed to this report.