Watson suffered the injury to his right throwing shoulder while running the ball Sunday against the Tennessee Titans.
Though Watson was limited in practice all week, Browns coach Kevin Stefanski said after Friday's practice that he's "hopeful" Watson can still play.
Watson barely threw during the portion of Friday's practice open to the media, but Stefanski said Watson did some "light" throwing later in the day.
If Watson is ruled out, rookie Dorian Thompson-Robinson will get the start in his place. Thompson-Robinson, a fifth-round pick out of UCLA, became the backup during the preseason after the Browns traded Joshua Dobbs to the Arizona Cardinals.
Watson had his best game in a Browns uniform last weekend. He completed 27 of 33 passes for 289 yards and two touchdowns in Cleveland's 27-3 win.