McCown missed last week's game against the Pittsburgh Steelers after tearing a ligament in his thumb against the Atlanta Falcons the week before. He sustained the injury when he hit his throwing hand on a defender's helmet after releasing a pass.
McCown didn't practice on Wednesday due to the injury.
It was reported at the time of his injury that McCown would miss at least one game. There was some question as to whether McCown may eventually need surgery, but according to Stroud there are still no plans for any operation.
In McCown's absence last week, backup quarterback Mike Glennon filled in and led the team to a 27-24 win, throwing for 302 yards, two touchdowns and one interception.
Glennon will also start this week's game against the Saints. Despite the backup's performance against Pittsburgh, head coach Lovie Smith said Monday that Glennon hadn't won the quarterback job going forward.
"You asking me to name our starting quarterback right now? What I do is I look at who's available at the time and who gives us our best chance to win at all positions,'' Smith said. "We'll do the same thing when Josh gets back. He's not back yet, though.
Glennon also started 13 games as a rookie last season, throwing for 2,608 yards, 19 touchdowns and nine interceptions.
The team signed McCown this offseason to a two-year, $10 million deal to be Tampa Bay's starting quarterback after throwing 13 touchdowns and just one interception in eight games and five starts for the Chicago Bears last season.
McCown, 35, has 420 passing yards, two touchdowns and four interceptions this season.
The win over the Steelers came after the Buccaneers were blown out by the Falcons 56-14.
- Ben Estes