Watson, who met with the Saints on Tuesday, recorded a team-leading 61 receptions with the Baltimore Ravens last season after missing all of 2016 with an Achilles injury. He also had 522 receiving yards and four touchdowns in 2017.
The 37-year-old Watson played with the Saints from 2013-15, highlighted by a career season in 2015 after the team traded fellow tight end Jimmy Graham to the Seattle Seahawks. Watson finished with 74 receptions for 825 yards and six touchdowns.
Watson would join a team that features a tight end corps comprised of Coby Fleener, Josh Hill, Michael Hoomanawanui, Garrett Griffin and Alex Ellis.
Watson has reeled in 495 catches for 5,485 yards and 42 touchdowns in 179 career games since being selected by the New England Patriots with the 32nd overall pick of the 2004 NFL Draft.