Prior to the Buccaneers releasing the injury report Friday, coach Todd Bowles had said that Smith faced tough odds to make it on the field in New Orleans. Neither Godwin nor Smith practiced this week.
"Donovan will be close. It will be hard for him to make it, but we'll see," Bowles told reporters. "Rest of the guys, we'll see on Sunday."
Four other wide receivers -- Mike Evans (calf), Russell Gage (hamstring), Julio Jones (knee) and Breshad Perriman -- are listed as questionable to play, as are running back Leonard Fournette (hamstring) and right tackle Tristan Wirfs (abdomen).
Godwin suffered a hamstring injury Sunday at the Dallas Cowboys -- his first game back since suffering a torn ACL and MCL against the Saints in Week 15 last season. Bowles had said he would guess that Godwin would be out against New Orleans.
Smith suffered a hyperextended right elbow against the Cowboys, leaving the game in the second quarter and not returning. Backup swing tackle Josh Wells, who has been practicing in Smith's spot all week, would get the start if Smith cannot go and misses a start for just the third time in 112 career games.
The Buccaneers haven't won in New Orleans in the regular season since Dec. 31, 2017. In their seven consecutive regular-season losses to the Saints, they have been outscored 210-108. The Buccaneers' lone win in that span came during the 2020 postseason, when they defeated the Saints 30-20 in the NFC divisional playoff.