Hill recently had surgery to repair a finger on his left hand that had become locked at a "90-degree angle," according to Nick Underhill of The New Orleans Advocate.
Hill caught 16 passes for 125 yards and a touchdown in the regular season without missing a game. The 27-year-old tight end added some key plays in the playoffs, snagging six passes for 103 yards and a touchdown in two postseason tilts.
Hill has one year remaining on a three-year deal signed in 2016. Tight end is one position the Saints could look to upgrade this offseason.