Shurmur told reporters Thursday that Hillis, who didn't practice Wednesday because of a strained left hamstring, is "day to day" and was expected to do some running in a pool. Hillis sustained the injury during last Sunday's loss at Oakland.
While Hillis is sidelined, there's also the lingering issue of his contract status. Browns president Mike Holmgren said Thursday the ongoing talks with the soon-to-be free agent continue to be at a standstill.
Hillis isn't the team's only injury concern this week. Starting linebacker Scott Fujita is unlikely to play Sunday after being sent home for a second consecutive day with post-concussion symptoms.
Fujita, who also was injured at Oakland, was sent home before Wednesday's practice, too. Shurmur wouldn't discuss specifics of Fujita's symptoms and didn't rule him out of this week's game against Seattle, but it's unlikely the linebacker would be medically cleared to play this late in the week if he's still having symptoms.
Shurmur didn't know if the 10-year veteran has sustained prior concussions.
The Associated Press contributed to this report.