Hill reportedly received all the starter reps in practice this week, Schefter adds.
Winston will not be part of any offensive packages for the Week 11 matchup, according to ESPN's Dianna Russini.
The decision comes as a bit of a surprise as the Saints rolled with Winston in relief of Drew Brees in each of their last two contests.
Brees reportedly suffered a collapsed lung and multiple rib fractures last week. The most optimistic timeline for his recovery is apparently two-to-three weeks.
Hill has primarily been used as a rushing threat in New Orleans' offense, though he's also played as a receiver. The 30-year-old has four rushing touchdowns and seven receiving scores over his career.
Hill has completed 10 of 18 career pass attempts for 205 yards. He has one interception but has yet to throw for a touchdown.