However, he must be cleared by an independent neurologist before he can play in a game after suffering a concussion against the Pittsburgh Steelers on Nov. 24. The Browns visit the New England Patriots this week.
Campbell will get some reps at practice Thursday, along with the other quarterbacks, and if he's cleared in time and coaches feel good about his situation from a game-plan standpoint, he would start Sunday.
"He still has not and will not pass the independent neurologist test until we see how he does today," Coach Rob Chudzinski said. "In the next 24-to-48 hours, obviously we would have more information on that. But he would need to pass that before he would be cleared to play in the game."
Offensive coordinator Norv Turner said Campbell has been "real sharp" in the team's meetings.
"Just getting him back in the walkthrough, I think everyone felt a sense of relief in that there was some continuity. Now we're gonna work all three guys and make sure we've covered all the bases in terms of getting ready," he said.
Veteran quarterback Caleb Hanie, who signed with the Browns earlier this week, and Alex Tanney, who was signed last week off the Dallas Cowboys' practice squad, split first-team reps in practice Wednesday.
Chudzinski said Wednesday that he might wait until Friday, or even right up until game time Sunday to make a decision.
ESPN.com Browns reporter Pat McManamon and ESPN NFL Insider Adam Schefter contributed to this report.