Jeff Howe of The Athletic reported Gillislee and the Saints will talk about a contract during his visit Sunday.
The Patriots released Gillislee as part of their 53-man roster cuts.
The Saints are looking to bolster their running back depth while Mark Ingram serves a four-game suspension for performance-enhancing drug use. They released Jonathan Williams as part of their 53-man cuts, a surprise move given most expected Williams to play a significant role with Ingram out.
Alvin Kamara is the team's primary pass-catcher out of the backfield and had a monster rookie season, but his size (5'10", 215 lbs) makes it a little questionable whether he can withstand a full workload. Rookie sixth-round pick Boston Scott could also play a pivotal role in the backfield.
In his sixth NFL season, Gillislee previously played for the Miami Dolphins and Buffalo Bills in addition to New England. He had his strongest season in 2016 with Buffalo, rushing for 577 yards and eight touchdowns on 101 carries.
The Patriots brought him in last year in hopes of finding a replacement for LeGarrette Blount, but he missed seven games and did not have a carry over 16 yards.
The Saints would likely view Gillislee as a short-yardage back and potentially turn to him on first and second downs in case of an injury. He's not much of a pass-catcher out of the backfield, so he'll remain at his most productive in a platoon.